Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11763531 | C2 | semidirect |
| 2. #11763202 | C2 | semidirect |
| 4. #11763031 | C2 | semidirect |
| 6. #11763018 | C2 | semidirect |
| 7. #11762939 | C2 | semidirect |
| 8. #11762908 | C2 | semidirect |
| 9. C4×Q16×C17 | C2 | semidirect |
| 107. C4×Q16 | D17 | semidirect |
| 137. C17 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763531 | 2 |
| #11763202 | 2 |
| #11763193 | 2 |
| #11763031 | 2 |
| #11763027 | 2 |
| #11763018 | 2 |
| #11762939 | 2 |
| #11762908 | 2 |
| C4×Q16×C17 | 2 |
| #3402 | 17 |