Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1072 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 287 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. C23×#3633 | C2 | semidirect |
| 2. C2×C22⋊#3633 | C2 | direct (N × H) |
| 11. C22×#3633 | C22 | semidirect |
| 12. C22⋊#3633 | C22 | direct (N × H) |
| 13. C24×C17 | C8 | semidirect |
| 16. C23×D17 | C8 | semidirect |
| 17. C23×D17 | C8 | semidirect |
| 30. C2×#3633 | C23 | semidirect |
| 33. C23×C17 | C2×C8 | semidirect |
| 40. C22×D17 | C2×C8 | semidirect |
| 41. C22×D17 | C2×C8 | semidirect |
| 56. C22×C17 | C22⋊C8 | semidirect |
| 58. C22×C17 | C22×C8 | semidirect |
| 63. C2×D17 | C22⋊C8 | semidirect |
| 66. C2×D17 | C22×C8 | semidirect |
| 76. C2×C17 | C2×C22⋊C8 | semidirect |
| 79. D17 | C2×C22⋊C8 | semidirect |
| 91. C17 | C22×C22⋊C8 | semidirect |
| 98. C24 | #3633 | semidirect |
| 123. C23 | C2×#3633 | semidirect |
| 144. C22 | C22⋊#3633 | direct (N × H) |
| 146. C22 | C22×#3633 | semidirect |
| 155. C2 | C2×C22⋊#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3633 | 2 |
| C2×C22⋊#3633 | 2 |
| C24×#595 | 2 |
| C22×C22⋊C8 | 17 |