Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 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×#10587530 | C2 | semidirect |
| 2. #11763865 | C2 | direct (N × H) |
| 3. C2×#10587538 | C2 | semidirect |
| 4. C2×#10587529 | C2 | semidirect |
| 15. #10587538 | C22 | semidirect |
| 16. C2×#63216 | C22 | semidirect |
| 17. #10587530 | C22 | semidirect |
| 18. #10587529 | C22 | semidirect |
| 41. #63216 | C23 | semidirect |
| 71. C2×D17 | M32 | semidirect |
| 85. C2×C17 | C2×M32 | semidirect |
| 88. D17 | C2×M32 | semidirect |
| 102. C17 | C22×M32 | semidirect |
| 165. C2 | #11763865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587530 | 2 |
| #11763865 | 2 |
| C2×#10587538 | 2 |
| C2×#10587529 | 2 |
| C22×C8×D17 | 2 |
| C22×M32 | 17 |