Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#10587493 | C2 | semidirect |
| 3. #11762813 | C2 | semidirect |
| 4. C2×#10587504 | C2 | semidirect |
| 5. C2×#10587494 | C2 | semidirect |
| 6. #11762765 | C2 | semidirect |
| 7. C17×#418 | C2 | semidirect |
| 15. C2×#63228 | C4 | semidirect |
| 109. #418 | D17 | semidirect |
| 137. C17 | #1978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| C2×#10587493 | 2 |
| #11762813 | 2 |
| C2×#10587504 | 2 |
| C2×#10587494 | 2 |
| #11762765 | 2 |
| C17×#418 | 2 |
| #1978 | 17 |