Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
456 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 164 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. #11763838 | C2 | semidirect |
| 2. #11763830 | C2 | semidirect |
| 3. #11763780 | C2 | semidirect |
| 4. C2×C22⋊#3624 | C2 | semidirect |
| 9. C22×#3624 | C22 | semidirect |
| 10. C2×#63243 | C22 | semidirect |
| 18. C22⋊#3624 | C22 | semidirect |
| 19. #10587543 | C22 | semidirect |
| 20. #10587542 | C22 | semidirect |
| 21. C4⋊#3624 | C22 | semidirect |
| 47. C23×C17 | M16 | semidirect |
| 117. C17 | #2973 | semidirect |
| 147. C23 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763838 | 2 |
| #11763830 | 2 |
| #11763780 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×#10587567 | 2 |
| #2973 | 17 |