Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14533730 | C2 | semidirect |
| 3. #14527453 | C2 | semidirect |
| 4. #14527279 | C2 | semidirect |
| 5. #14527175 | C2 | semidirect |
| 6. #14526685 | C2 | semidirect |
| 7. C17×#3036 | C2 | semidirect |
| 43. C17×C4⋊Q8 | D4 | semidirect |
| 44. C17×#127 | D4 | semidirect |
| 69. C17×C4⋊C8 | D4 | semidirect |
| 77. C4⋊#3622 | D4 | semidirect |
| 96. C2×D4×C17 | D8 | semidirect |
| 205. #3036 | D17 | semidirect |
| 284. C4⋊Q8 | C22⋊D17 | semidirect |
| 291. #127 | C22⋊D17 | semidirect |
| 311. C4⋊C8 | C22⋊D17 | semidirect |
| 320. C17 | #10238 | semidirect |
| 352. C2×D4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539699 | 2 |
| #14533730 | 2 |
| #14527453 | 2 |
| #14527279 | 2 |
| #14527175 | 2 |
| #14526685 | 2 |
| C17×#3036 | 2 |
| #10238 | 17 |