Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 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×#595 | C2 | semidirect |
| 3. C2×C22⋊#595 | C2 | semidirect |
| 4. C2×C22⋊#595 | C2 | semidirect |
| 5. (C2×#595)⋊C4 | C2 | semidirect |
| 12. C2×D4×C17 | C4 | semidirect |
| 13. C2×C22⋊D17 | C4 | semidirect |
| 14. C2×C22⋊D17 | C4 | semidirect |
| 17. C2×D68 | C4 | semidirect |
| 22. C23×C17 | C2×C4 | semidirect |
| 30. C22×D17 | C2×C4 | semidirect |
| 40. C2×#595 | D4 | semidirect |
| 42. C2×C4×C17 | C2×C4 | semidirect |
| 45. C2×Dic17 | C2×C4 | semidirect |
| 52. C22×C17 | C22⋊C4 | semidirect |
| 63. C2×D17 | C22⋊C4 | semidirect |
| 87. C17 | #386 | semidirect |
| 95. C2×D4 | #595 | semidirect |
| 115. C23 | C2×#595 | semidirect |
| 130. C2×C4 | C2×#595 | semidirect |
| 148. C22 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#595 | 2 |
| C2×D4×D17 | 2 |
| C2×C22⋊#595 | 2 |
| (C2×#595)⋊C4 | 2 |
| #386 | 17 |