Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1138 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#11763557 | C2 | semidirect |
| 2. C2×#11763196 | C2 | semidirect |
| 3. #14528076 | C2 | direct (N × H) |
| 4. C2×#11762551 | C2 | semidirect |
| 5. C2×#11762548 | C2 | semidirect |
| 6. C2×C17×#490 | C2 | semidirect |
| 11. #11763557 | C22 | semidirect |
| 17. #11763196 | C22 | semidirect |
| 19. #11762551 | C22 | semidirect |
| 20. #11762548 | C22 | semidirect |
| 24. C17×#490 | C22 | semidirect |
| 143. C2×#490 | D17 | semidirect |
| 177. #490 | C2×D17 | semidirect |
| 184. C2×C17 | #1656 | semidirect |
| 228. C17 | C2×#1656 | semidirect |
| 320. C2 | #14528076 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763557 | 2 |
| C2×#11763196 | 2 |
| #14528076 | 2 |
| C2×#11762551 | 2 |
| C2×#11762548 | 2 |
| C2×C17×#490 | 2 |
| C2×#1656 | 17 |