Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
452 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 156 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. #11763844 | C2 | semidirect |
| 2. #11763843 | C2 | semidirect |
| 3. #11763842 | C2 | semidirect |
| 4. #11763828 | C2 | semidirect |
| 5. #11763827 | C2 | semidirect |
| 6. #11763781 | C2 | semidirect |
| 7. #11763780 | C2 | semidirect |
| 11. C2×#63247 | C22 | semidirect |
| 12. C2×#63243 | C22 | semidirect |
| 22. C22⋊#3624 | C22 | semidirect |
| 23. #10587544 | C22 | semidirect |
| 27. #10587543 | C22 | semidirect |
| 28. C4⋊#3624 | C22 | semidirect |
| 29. C4×#3624 | C22 | semidirect |
| 30. C4×#3624 | C22 | semidirect |
| 85. C4×D17 | M16 | semidirect |
| 145. C17 | #2975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763844 | 2 |
| #11763843 | 2 |
| #11763842 | 2 |
| #11763828 | 2 |
| #11763827 | 2 |
| #11763781 | 2 |
| #11763780 | 2 |
| C4×D4×D17 | 2 |
| #2975 | 17 |