Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #120 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×C4 | C23×C29 |
| socle | C2×C29 | #386 |
| prime radical | C29×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#568 | C2 | semidirect |
| 3. C29×#421 | C2 | semidirect |
| 4. C29×#410 | C2 | semidirect |
| 5. C29×#339 | C2 | semidirect |
| 11. C29×C4⋊Q8 | C4 | semidirect |
| 12. C29×#127 | C4 | semidirect |
| 13. C29×#124 | C4 | semidirect |
| 14. C29×#124 | C4 | semidirect |
| 38. M16×C29 | D4 | semidirect |
| 75. #1884 | C29 | direct (N × H) |
| 91. #568 | C2×C29 | semidirect |
| 93. #421 | C2×C29 | semidirect |
| 94. #410 | C2×C29 | semidirect |
| 95. #339 | C2×C29 | semidirect |
| 106. C4⋊Q8 | C4×C29 | semidirect |
| 107. #127 | C4×C29 | semidirect |
| 108. #124 | C4×C29 | semidirect |
| 109. #124 | C4×C29 | semidirect |
| 116. C29 | #1884 | direct (N × H) |
| 134. M16 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#568 | 2 |
| C29×#532 | 2 |
| C29×#421 | 2 |
| C29×#410 | 2 |
| C29×#339 | 2 |
| #1884 | 29 |