Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
406 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 168 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. #11763859 | C2 | semidirect |
| 2. #11763838 | C2 | semidirect |
| 3. D4×#3624 | C2 | semidirect |
| 4. #11763831 | C2 | semidirect |
| 5. #11763830 | C2 | semidirect |
| 6. C4×#63243 | C2 | semidirect |
| 7. C2×#10587542 | C2 | semidirect |
| 62. D4×C17 | M16 | semidirect |
| 82. #3624 | #41 | semidirect |
| 135. C17 | #2970 | semidirect |
| 169. D4 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763859 | 2 |
| #11763838 | 2 |
| D4×#3624 | 2 |
| #11763831 | 2 |
| #11763830 | 2 |
| C4×#63243 | 2 |
| C2×#10587542 | 2 |
| C4×#63254 | 2 |
| #2970 | 17 |