Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11763779 | C2 | semidirect |
| 2. #11763654 | C2 | semidirect |
| 3. #11763652 | C2 | semidirect |
| 49. C23×C17 | M16 | semidirect |
| 54. C2×C4×C17 | M16 | semidirect |
| 114. C17 | #1465 | semidirect |
| 146. C23 | #63247 | semidirect |
| 165. C2×C4 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763779 | 2 |
| #11763654 | 2 |
| #11763652 | 2 |
| C2×D4×Dic17 | 2 |
| #1465 | 17 |