Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 4. #11762562 | C2 | semidirect |
| 5. #11762558 | C2 | semidirect |
| 6. #11762555 | C2 | semidirect |
| 7. C17×#498 | C2 | semidirect |
| 56. C8×C17 | SD16 | semidirect |
| 73. #498 | D17 | semidirect |
| 99. C17 | #1691 | semidirect |
| 136. C8 | #63230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763096 | 2 |
| #11763011 | 2 |
| #11762888 | 2 |
| #11762562 | 2 |
| #11762558 | 2 |
| #11762555 | 2 |
| C17×#498 | 2 |
| #1691 | 17 |