Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11763837 | C2 | semidirect |
| 2. D4×#3624 | C2 | semidirect |
| 3. #11763673 | C2 | semidirect |
| 4. #11763657 | C2 | semidirect |
| 5. D4⋊#3624 | C2 | semidirect |
| 6. C8×#3624 | C2 | semidirect |
| 37. #63228 | C8 | semidirect |
| 45. D4×C17 | C2×C8 | semidirect |
| 54. D68 | C2×C8 | semidirect |
| 61. #3624 | D8 | semidirect |
| 63. #3622 | C2×C8 | semidirect |
| 106. C17 | C8×D8 | semidirect |
| 131. D4 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763837 | 2 |
| D4×#3624 | 2 |
| #11763673 | 2 |
| #11763657 | 2 |
| D4⋊#3624 | 2 |
| C8×#3624 | 2 |
| #11762889 | 2 |
| C8×D8 | 17 |