Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 191 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. D4×#3633 | C2 | semidirect |
| 2. #11763922 | C2 | semidirect |
| 3. C2×C22⋊#3633 | C2 | semidirect |
| 6. C22×#3633 | C22 | semidirect |
| 14. C22⋊#3633 | C22 | semidirect |
| 15. C4⋊#3633 | C22 | semidirect |
| 16. C4×#3633 | C22 | semidirect |
| 26. C2×D4×C17 | C8 | semidirect |
| 27. C2×C22⋊D17 | C8 | semidirect |
| 28. D4×D17 | C8 | semidirect |
| 30. C2×D68 | C8 | semidirect |
| 36. C23×C17 | C2×C8 | semidirect |
| 39. C22×D17 | C2×C8 | semidirect |
| 40. C22×D17 | C2×C8 | semidirect |
| 53. D4×C17 | C2×C8 | semidirect |
| 54. C2×C4×C17 | C2×C8 | semidirect |
| 55. C22⋊D17 | C2×C8 | semidirect |
| 56. C2×Dic17 | C2×C8 | semidirect |
| 57. D68 | C2×C8 | semidirect |
| 58. C4×D17 | C2×C8 | semidirect |
| 102. C17 | #2972 | semidirect |
| 108. C2×D4 | #3633 | semidirect |
| 128. C23 | C2×#3633 | semidirect |
| 131. D4 | C2×#3633 | semidirect |
| 144. C2×C4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#3633 | 2 |
| #11763922 | 2 |
| C2×C22⋊#3633 | 2 |
| C2×D4×#595 | 2 |
| #2972 | 17 |