Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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. #14272191 | C2 | semidirect |
| 2. #14272179 | C2 | semidirect |
| 3. D29⋊(C22⋊C8) | C2 | semidirect |
| 7. C2×D29⋊C8 | C22 | semidirect |
| 14. #11745219 | C22 | semidirect |
| 15. C4⋊#6599 | C22 | semidirect |
| 16. C4×#6599 | C22 | semidirect |
| 22. C2×D116 | C8 | semidirect |
| 36. C22×D29 | C2×C8 | semidirect |
| 39. C2×C4×C29 | C2×C8 | semidirect |
| 47. D116 | C2×C8 | semidirect |
| 86. C29 | #2972 | semidirect |
| 117. C2×C4 | D29⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272191 | 2 |
| #14272179 | 2 |
| D29⋊(C22⋊C8) | 2 |
| C2×#11745255 | 2 |
| #2972 | 29 |