Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
590 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 96 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×D8×#595 | C2 | semidirect |
| 2. C2×#11763721 | C2 | semidirect |
| 3. C2×#11763721 | C2 | semidirect |
| 4. #14544931 | C2 | semidirect |
| 5. #14543842 | C2 | semidirect |
| 6. #14543821 | C2 | semidirect |
| 22. C2×D272 | C4 | semidirect |
| 23. C2×#10587497 | C4 | semidirect |
| 24. C2×#10587497 | C4 | semidirect |
| 28. C2×C17×D16 | C4 | semidirect |
| 42. C2×D8×C17 | C2×C4 | semidirect |
| 54. C2×D136 | C2×C4 | semidirect |
| 68. C2×C16×C17 | C2×C4 | semidirect |
| 71. C2×#63214 | C2×C4 | semidirect |
| 114. D8×C17 | C22⋊C4 | semidirect |
| 124. D136 | C22⋊C4 | semidirect |
| 162. C2×#595 | D16 | semidirect |
| 236. C2×D16 | #595 | semidirect |
| 276. C2×D8 | C2×#595 | semidirect |
| 297. C2×C16 | C2×#595 | semidirect |
| 306. C17 | #13012 | semidirect |
| 342. D8 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#595 | 2 |
| C2×#11763721 | 2 |
| #14544931 | 2 |
| #14543842 | 2 |
| #14543821 | 2 |
| C2×D16×D17 | 2 |
| #13012 | 17 |