Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
422 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 152 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. #11763840 | C2 | semidirect |
| 2. #11763838 | C2 | semidirect |
| 3. #11763836 | C2 | semidirect |
| 4. D4×#3624 | C2 | semidirect |
| 5. #11763833 | C2 | semidirect |
| 6. #11763783 | C2 | semidirect |
| 7. #11763782 | C2 | semidirect |
| 8. C2×C22⋊#3624 | C2 | semidirect |
| 12. C2×#63247 | C22 | semidirect |
| 15. C22×#3624 | C22 | semidirect |
| 16. C2×#63243 | C22 | semidirect |
| 17. C2×#63242 | C22 | semidirect |
| 31. C22⋊#3624 | C22 | semidirect |
| 32. #10587544 | C22 | semidirect |
| 33. #10587543 | C22 | semidirect |
| 34. #10587542 | C22 | semidirect |
| 35. C4⋊#3624 | C22 | semidirect |
| 36. C4×#3624 | C22 | semidirect |
| 169. C17 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763840 | 2 |
| #11763838 | 2 |
| #11763836 | 2 |
| D4×#3624 | 2 |
| #11763833 | 2 |
| #11763783 | 2 |
| #11763782 | 2 |
| C2×C22⋊#3624 | 2 |
| #11763315 | 2 |
| #2977 | 17 |