Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
668 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C29 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×SD16×C29 | C2 | semidirect |
| 2. C22×D8×C29 | C2 | semidirect |
| 3. C2×C29×#127 | C2 | semidirect |
| 4. C2×C29×#124 | C2 | semidirect |
| 5. C29×#496 | C2 | direct (N × H) |
| 6. C2×C29×#97 | C2 | semidirect |
| 12. C2×SD16×C29 | C22 | semidirect |
| 14. C2×D8×C29 | C22 | semidirect |
| 17. C29×#127 | C22 | semidirect |
| 19. C29×#124 | C22 | semidirect |
| 22. C29×#97 | C22 | semidirect |
| 42. C2×C8×C29 | D4 | semidirect |
| 69. C8×C29 | C2×D4 | semidirect |
| 70. C2×#496 | C29 | direct (N × H) |
| 84. C22×SD16 | C2×C29 | semidirect |
| 85. C22×D8 | C2×C29 | semidirect |
| 86. C2×#127 | C2×C29 | semidirect |
| 87. C2×#124 | C2×C29 | semidirect |
| 88. #496 | C2×C29 | direct (N × H) |
| 89. C2×#97 | C2×C29 | semidirect |
| 92. C2×C29 | #496 | direct (N × H) |
| 100. C2×SD16 | C22×C29 | semidirect |
| 102. C2×D8 | C22×C29 | semidirect |
| 105. #127 | C22×C29 | semidirect |
| 107. #124 | C22×C29 | semidirect |
| 110. #97 | C22×C29 | semidirect |
| 111. C29 | C2×#496 | direct (N × H) |
| 131. C2×C8 | D4×C29 | semidirect |
| 158. C8 | C2×D4×C29 | semidirect |
| 174. C2 | C29×#496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C29 | 2 |
| C22×D8×C29 | 2 |
| C2×C29×#127 | 2 |
| C2×C29×#124 | 2 |
| C29×#496 | 2 |
| C2×C29×#97 | 2 |
| C2×#496 | 29 |