Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
272 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 74 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×#10587529 | C2 | semidirect |
| 2. C2×#10587534 | C2 | semidirect |
| 3. #11763721 | C2 | direct (N × H) |
| 7. C2×D8×C17 | C4 | semidirect |
| 11. D8×D17 | C4 | semidirect |
| 13. C2×D136 | C4 | semidirect |
| 17. #10587534 | C22 | semidirect |
| 19. #10587529 | C22 | semidirect |
| 33. D8×C17 | C2×C4 | semidirect |
| 39. D136 | C2×C4 | semidirect |
| 93. C2×C17 | #357 | semidirect |
| 96. D17 | #357 | semidirect |
| 106. C2×D8 | #595 | semidirect |
| 114. C17 | C2×#357 | semidirect |
| 130. D8 | C2×#595 | semidirect |
| 187. C2 | #11763721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587529 | 2 |
| C2×#10587534 | 2 |
| #11763721 | 2 |
| C2×D8×D17 | 2 |
| C2×#357 | 17 |