Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #14538244 | C2 | semidirect |
| 2. #14533731 | C2 | semidirect |
| 3. #14527452 | C2 | semidirect |
| 4. #14527279 | C2 | semidirect |
| 5. #14527174 | C2 | semidirect |
| 6. #14526686 | C2 | semidirect |
| 7. C17×#3205 | C2 | semidirect |
| 39. C17×C4⋊Q8 | D4 | semidirect |
| 44. C17×#127 | D4 | semidirect |
| 68. C17×C4⋊C8 | D4 | semidirect |
| 78. C4⋊#3622 | D4 | semidirect |
| 117. C2×D68 | D8 | semidirect |
| 204. #3205 | D17 | semidirect |
| 284. C4⋊Q8 | C22⋊D17 | semidirect |
| 291. #127 | C22⋊D17 | semidirect |
| 311. C4⋊C8 | C22⋊D17 | semidirect |
| 320. C17 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538244 | 2 |
| #14533731 | 2 |
| #14527452 | 2 |
| #14527279 | 2 |
| #14527174 | 2 |
| #14526686 | 2 |
| C17×#3205 | 2 |
| #10238 | 17 |