Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#10587618 | C2 | semidirect |
| 2. #11763376 | C2 | semidirect |
| 3. C2×#10587476 | C2 | semidirect |
| 4. #11762814 | C2 | semidirect |
| 5. C2×#10587504 | C2 | semidirect |
| 6. #11762569 | C2 | semidirect |
| 7. C2×C17×#127 | C2 | semidirect |
| 44. C2×D4×C17 | D4 | semidirect |
| 53. C2×D68 | D4 | semidirect |
| 55. C2×Dic34 | D4 | semidirect |
| 57. C42×C17 | D4 | semidirect |
| 62. C4⋊Dic17 | D4 | semidirect |
| 67. #63223 | D4 | semidirect |
| 134. C2×#127 | D17 | semidirect |
| 167. C17 | #2002 | semidirect |
| 191. C2×D4 | C22⋊D17 | semidirect |
| 208. C42 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587618 | 2 |
| #11763376 | 2 |
| C2×#10587476 | 2 |
| #11762814 | 2 |
| C2×#10587504 | 2 |
| #11762569 | 2 |
| C2×C17×#127 | 2 |
| #2002 | 17 |