Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
144 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 144 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. #11763851 | C2 | semidirect |
| 3. #11763737 | C2 | semidirect |
| 4. #11763724 | C2 | semidirect |
| 5. #11763723 | C2 | semidirect |
| 6. #11763696 | C2 | semidirect |
| 18. C17×SD32 | C4 | semidirect |
| 19. #10587500 | C4 | semidirect |
| 20. #10587497 | C4 | semidirect |
| 21. #10587471 | C4 | semidirect |
| 85. SD32 | #595 | semidirect |
| 94. C17 | #2179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763853 | 2 |
| #11763851 | 2 |
| #11763737 | 2 |
| #11763724 | 2 |
| #11763723 | 2 |
| #11763696 | 2 |
| #11763240 | 2 |
| #2179 | 17 |