Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14538780 | C2 | semidirect |
| 2. #14538244 | C2 | semidirect |
| 3. #14533686 | C2 | semidirect |
| 4. #14527210 | C2 | semidirect |
| 5. #14527174 | C2 | semidirect |
| 6. #14526642 | C2 | semidirect |
| 7. C17×#1517 | C2 | semidirect |
| 39. C17×C4⋊Q8 | D4 | semidirect |
| 40. C17×#127 | D4 | semidirect |
| 84. C4⋊#3622 | D4 | semidirect |
| 85. C4×#3622 | D4 | semidirect |
| 115. C2×D68 | D8 | semidirect |
| 220. #1517 | D17 | semidirect |
| 301. C4⋊Q8 | D68 | semidirect |
| 302. #127 | D68 | semidirect |
| 342. C17 | #9996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538780 | 2 |
| #14538244 | 2 |
| #14533686 | 2 |
| #14527210 | 2 |
| #14527174 | 2 |
| #14526642 | 2 |
| C17×#1517 | 2 |
| #9996 | 17 |