Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 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×#11763186 | C2 | semidirect |
| 2. C2×#11763185 | C2 | semidirect |
| 3. #14528398 | C2 | direct (N × H) |
| 4. C2×C8×#3622 | C2 | semidirect |
| 5. C2×C17×#493 | C2 | semidirect |
| 10. #11763186 | C22 | semidirect |
| 12. #11763185 | C22 | semidirect |
| 14. C8×#3622 | C22 | semidirect |
| 18. C17×#493 | C22 | semidirect |
| 60. C2×C8×C17 | D8 | semidirect |
| 66. C2×#3622 | D8 | semidirect |
| 91. C8×C17 | C2×D8 | semidirect |
| 92. #3622 | C2×D8 | semidirect |
| 95. C2×#493 | D17 | semidirect |
| 121. #493 | C2×D17 | semidirect |
| 126. C2×C17 | #1712 | semidirect |
| 153. C17 | C2×#1712 | semidirect |
| 175. C2×C8 | #63228 | semidirect |
| 202. C8 | C2×#63228 | semidirect |
| 218. C2 | #14528398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763186 | 2 |
| C2×#11763185 | 2 |
| #14528398 | 2 |
| C2×C8×#3622 | 2 |
| C2×C17×#493 | 2 |
| C2×#1712 | 17 |