Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10587489 | C2 | semidirect |
| 4. #11762708 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 20. C17×#102 | C4 | semidirect |
| 42. C2×C8×C17 | C2×C4 | semidirect |
| 44. C4⋊C4×C17 | C2×C4 | semidirect |
| 67. D4×C17 | C4⋊C4 | semidirect |
| 145. #102 | Dic17 | semidirect |
| 147. C17 | #1862 | semidirect |
| 169. C2×C8 | C2×Dic17 | semidirect |
| 176. C4⋊C4 | C2×Dic17 | semidirect |
| 191. D4 | C4⋊Dic17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic17 | 2 |
| C2×#10587489 | 2 |
| C2×#10587503 | 2 |
| #11762708 | 2 |
| #11762571 | 2 |
| #11762563 | 2 |
| C2×C17×#102 | 2 |
| #1862 | 17 |