Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
402 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 156 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. #14272187 | C2 | semidirect |
| 2. #14272185 | C2 | semidirect |
| 3. #14272181 | C2 | semidirect |
| 4. #14272170 | C2 | semidirect |
| 7. #14272128 | C2 | semidirect |
| 24. #11745220 | C22 | semidirect |
| 28. #11745218 | C22 | semidirect |
| 29. C4⋊#6599 | C22 | semidirect |
| 30. C4×#6599 | C22 | semidirect |
| 141. C29 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272187 | 2 |
| #14272185 | 2 |
| #14272181 | 2 |
| #14272170 | 2 |
| #14272134 | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272128 | 2 |
| #117×D29 | 2 |
| #2924 | 29 |