Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14545909 | C2 | semidirect |
| 4. M16×#3633 | C2 | semidirect |
| 5. #14545796 | C2 | semidirect |
| 6. #14545791 | C2 | semidirect |
| 59. C17×#100 | C8 | semidirect |
| 60. #10587504 | C8 | semidirect |
| 61. #10587494 | C8 | semidirect |
| 62. #10587494 | C8 | semidirect |
| 232. #100 | #3633 | semidirect |
| 244. C17 | #9550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545909 | 2 |
| #14545904 | 2 |
| C2×D4⋊#3633 | 2 |
| M16×#3633 | 2 |
| #14545796 | 2 |
| #14545791 | 2 |
| #100×#595 | 2 |
| #9550 | 17 |