Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1074 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 219 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×#11763188 | C2 | semidirect |
| 2. C2×#11763099 | C2 | semidirect |
| 3. #14527929 | C2 | direct (N × H) |
| 4. C2×#11762558 | C2 | semidirect |
| 5. C2×D4⋊#3622 | C2 | semidirect |
| 10. #11763188 | C22 | semidirect |
| 12. #11763099 | C22 | semidirect |
| 17. #11762558 | C22 | semidirect |
| 18. D4⋊#3622 | C22 | semidirect |
| 179. C2×C17 | #1634 | semidirect |
| 220. C17 | C2×#1634 | semidirect |
| 308. C2 | #14527929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763188 | 2 |
| C2×#11763099 | 2 |
| #14527929 | 2 |
| C2×#11762558 | 2 |
| C2×D4⋊#3622 | 2 |
| C2×C17×#555 | 2 |
| C2×#1634 | 17 |