Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #11763853 | C2 | semidirect |
| 2. #11763737 | C2 | semidirect |
| 3. #11763724 | C2 | semidirect |
| 4. C16×#595 | C2 | semidirect |
| 12. C17×Q32 | C4 | semidirect |
| 13. #10587499 | C4 | semidirect |
| 14. D272 | C4 | semidirect |
| 57. Q32 | #595 | semidirect |
| 65. C17 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763853 | 2 |
| #11763737 | 2 |
| #11763724 | 2 |
| C16×#595 | 2 |
| #11763242 | 2 |
| #2178 | 17 |