Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #11745301 |
| commutator, cosocle | C42×C29 | C23 |
| Frattini | C42 | C22×D29 |
| Fitting | C29×#459 | C2 |
| socle | C22×C29 | #121 |
| hypercenter | #459 | D29 |
| hypocenter | C29 | #1667 |
| LCS | G ▷ C42×C29 ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271539 | C2 | semidirect |
| 2. #14271358 | C2 | semidirect |
| 3. D4×#6597 | C2 | semidirect |
| 4. #14270915 | C2 | semidirect |
| 5. #14270907 | C2 | semidirect |
| 6. #14270906 | C2 | semidirect |
| 7. C29×#459 | C2 | semidirect |
| 53. D4×C29 | D8 | semidirect |
| 69. #6597 | D8 | semidirect |
| 89. #459 | D29 | semidirect |
| 115. C29 | #1667 | semidirect |
| 151. D4 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271539 | 2 |
| #14271358 | 2 |
| D4×#6597 | 2 |
| #14270915 | 2 |
| #14270907 | 2 |
| #14270906 | 2 |
| C29×#459 | 2 |
| #1667 | 29 |