Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D68 | C2 | semidirect |
| 2. #14531034 | C2 | semidirect |
| 3. #14530819 | C2 | semidirect |
| 4. #14528140 | C2 | semidirect |
| 5. #14526829 | C2 | semidirect |
| 6. #14526740 | C2 | semidirect |
| 7. C17×#1331 | C2 | semidirect |
| 13. #11763186 | C22 | semidirect |
| 19. C4⋊#63214 | C22 | semidirect |
| 23. C4×C16×C17 | C22 | semidirect |
| 24. C17×#335 | C22 | semidirect |
| 74. D8×C17 | D8 | semidirect |
| 127. D68 | D16 | semidirect |
| 140. #1331 | D17 | semidirect |
| 177. C4×C16 | C2×D17 | semidirect |
| 178. #335 | C2×D17 | semidirect |
| 218. C17 | #12316 | semidirect |
| 245. D8 | D136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D68 | 2 |
| #14531034 | 2 |
| #14530819 | 2 |
| #14528140 | 2 |
| #14526829 | 2 |
| #14526740 | 2 |
| C17×#1331 | 2 |
| #12316 | 17 |