Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11763156 | C2 | semidirect |
| 3. #11763090 | C2 | semidirect |
| 4. #11763019 | C2 | semidirect |
| 5. #11762552 | C2 | semidirect |
| 6. #11762538 | C2 | semidirect |
| 7. C17×Q8⋊C8 | C2 | semidirect |
| 100. Q8⋊C8 | D17 | semidirect |
| 124. C17 | #1641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763481 | 2 |
| #11763156 | 2 |
| #11763090 | 2 |
| #11763019 | 2 |
| #11762552 | 2 |
| #11762538 | 2 |
| C17×Q8⋊C8 | 2 |
| #1641 | 17 |