Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #14539699 | C2 | semidirect |
| 2. #14538244 | C2 | semidirect |
| 3. #14533726 | C2 | semidirect |
| 4. #14527451 | C2 | semidirect |
| 5. #14527176 | C2 | semidirect |
| 6. #14526687 | C2 | semidirect |
| 7. C17×#1502 | C2 | semidirect |
| 38. C17×C4⋊Q8 | D4 | semidirect |
| 39. C17×#127 | D4 | semidirect |
| 77. C4⋊#3622 | D4 | semidirect |
| 78. C4⋊#3622 | D4 | semidirect |
| 117. C2×D68 | D8 | semidirect |
| 208. #1502 | D17 | semidirect |
| 284. C4⋊Q8 | D68 | semidirect |
| 291. #127 | D68 | semidirect |
| 320. C17 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14538244 | 2 |
| #14533726 | 2 |
| #14527451 | 2 |
| #14527176 | 2 |
| #14526687 | 2 |
| C17×#1502 | 2 |
| #10238 | 17 |