Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#10587590 | C2 | semidirect |
| 2. #11763252 | C2 | semidirect |
| 3. #11763247 | C2 | semidirect |
| 4. #11763241 | C2 | semidirect |
| 5. C2×C17×M32 | C2 | semidirect |
| 8. C2×Dic68 | C22 | semidirect |
| 12. #10587590 | C22 | semidirect |
| 13. C2×D136 | C22 | semidirect |
| 15. C17×M32 | C22 | semidirect |
| 16. C2×C16×C17 | C22 | semidirect |
| 17. Dic136 | C22 | semidirect |
| 18. #10587471 | C22 | semidirect |
| 19. D272 | C22 | semidirect |
| 72. C2×M32 | D17 | semidirect |
| 89. M32 | C2×D17 | semidirect |
| 90. C2×C16 | C2×D17 | semidirect |
| 91. C17 | #3414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587590 | 2 |
| #11763252 | 2 |
| #11763247 | 2 |
| #11763241 | 2 |
| C2×C17×M32 | 2 |
| #3414 | 17 |