Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11763529 | C2 | semidirect |
| 2. #11763156 | C2 | semidirect |
| 3. #11763010 | C2 | semidirect |
| 5. #11762554 | C2 | semidirect |
| 6. #11762541 | C2 | semidirect |
| 7. C17×D4⋊C8 | C2 | semidirect |
| 97. D4⋊C8 | D17 | semidirect |
| 120. C17 | #1628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763529 | 2 |
| #11763156 | 2 |
| #11763010 | 2 |
| #11763004 | 2 |
| #11762554 | 2 |
| #11762541 | 2 |
| C17×D4⋊C8 | 2 |
| #1628 | 17 |