Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11763283 | C2 | semidirect |
| 3. #11762826 | C2 | semidirect |
| 4. C2×#10587494 | C2 | semidirect |
| 5. #11762566 | C2 | semidirect |
| 6. #11762565 | C2 | semidirect |
| 7. C17×#421 | C2 | semidirect |
| 12. #10587633 | C4 | semidirect |
| 13. #10587626 | C4 | semidirect |
| 30. C2×Q8×C17 | C2×C4 | semidirect |
| 32. C2×D4×C17 | C2×C4 | semidirect |
| 48. C42×C17 | D4 | semidirect |
| 55. C4×Dic17 | C2×C4 | semidirect |
| 56. C4×Dic17 | D4 | semidirect |
| 114. #421 | D17 | semidirect |
| 141. C17 | #1911 | semidirect |
| 147. C2×Q8 | C4×D17 | semidirect |
| 156. C2×D4 | C4×D17 | semidirect |
| 176. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763373 | 2 |
| #11763283 | 2 |
| #11762826 | 2 |
| C2×#10587494 | 2 |
| #11762566 | 2 |
| #11762565 | 2 |
| C17×#421 | 2 |
| #1911 | 17 |