Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
452 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 452 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. #11763843 | C2 | semidirect |
| 2. #11763825 | C2 | semidirect |
| 3. #11763780 | C2 | semidirect |
| 7. C2×#63243 | C22 | semidirect |
| 14. #10587543 | C22 | semidirect |
| 15. C4⋊#3624 | C22 | semidirect |
| 16. C4×#3624 | C22 | semidirect |
| 39. C2×C4×C17 | M16 | semidirect |
| 86. C17 | #2975 | semidirect |
| 117. C2×C4 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763843 | 2 |
| #11763825 | 2 |
| #11763780 | 2 |
| C2×#10587579 | 2 |
| #2975 | 17 |