Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#11745345 | C2 | semidirect |
| 2. C2×#11745223 | C2 | semidirect |
| 3. D29⋊(C22⋊C8) | C2 | semidirect |
| 4. #14272036 | C2 | semidirect |
| 14. C29×#121 | C4 | semidirect |
| 16. #11745300 | C4 | semidirect |
| 17. #11745292 | C4 | semidirect |
| 18. #11745257 | C4 | semidirect |
| 50. C4⋊#1181 | D4 | semidirect |
| 152. #121 | #1181 | semidirect |
| 162. C29 | #1875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745345 | 2 |
| C2×#11745223 | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272036 | 2 |
| #121×D29 | 2 |
| #1875 | 29 |