Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #99 |
| commutator | C2×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×D4 | C23×C29 |
| prime radical | C22×D4×C29 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C29 ◁ C22×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#354 | C2 | direct (N × H) |
| 4. C22×Q8×C29 | C4 | semidirect |
| 7. C29×#124 | C4 | semidirect |
| 11. C2×C42×C29 | C4 | semidirect |
| 18. C2×Q8×C29 | C2×C4 | semidirect |
| 33. C42×C29 | C2×C4 | semidirect |
| 56. C2×#354 | C29 | direct (N × H) |
| 74. #354 | C2×C29 | direct (N × H) |
| 79. C2×C29 | #354 | direct (N × H) |
| 81. C22×Q8 | C4×C29 | semidirect |
| 84. #124 | C4×C29 | semidirect |
| 88. C2×C42 | C4×C29 | semidirect |
| 91. C29 | C2×#354 | direct (N × H) |
| 96. C2×Q8 | C2×C4×C29 | semidirect |
| 111. C42 | C2×C4×C29 | semidirect |
| 153. C2 | C29×#354 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#124 | 2 |
| C2×C29×#99 | 2 |
| C29×#354 | 2 |
| C2×#354 | 29 |