Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
166 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271561 | C2 | semidirect |
| 4. #14270914 | C2 | semidirect |
| 5. #14270911 | C2 | semidirect |
| 6. #14270908 | C2 | semidirect |
| 57. C8×C29 | SD16 | semidirect |
| 99. C29 | #1671 | semidirect |
| 136. C8 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271561 | 2 |
| #14271453 | 2 |
| #14271368 | 2 |
| #14270914 | 2 |
| #14270911 | 2 |
| #14270908 | 2 |
| C8×D4×C29 | 2 |
| #1671 | 29 |