Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11763544 | C2 | semidirect |
| 2. #11763194 | C2 | semidirect |
| 4. #11763027 | C2 | semidirect |
| 5. #11763009 | C2 | semidirect |
| 6. C8×Dic34 | C2 | semidirect |
| 7. #11762891 | C2 | semidirect |
| 8. C4×Q16×C17 | C2 | semidirect |
| 89. C4×Q16 | D17 | semidirect |
| 114. C17 | #3396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763544 | 2 |
| #11763194 | 2 |
| #11763186 | 2 |
| #11763027 | 2 |
| #11763009 | 2 |
| C8×Dic34 | 2 |
| #11762891 | 2 |
| C4×Q16×C17 | 2 |
| #3396 | 17 |