Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1262 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 191 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. #14542555 | C2 | semidirect |
| 2. #14539702 | C2 | semidirect |
| 3. #14527718 | C2 | semidirect |
| 4. #14527278 | C2 | semidirect |
| 5. #14527108 | C2 | semidirect |
| 6. C17×#2548 | C2 | semidirect |
| 78. C2×Q8×C17 | D8 | semidirect |
| 171. #2548 | D17 | semidirect |
| 271. C17 | #18401 | semidirect |
| 283. C2×Q8 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14542555 | 2 |
| #14539702 | 2 |
| #14527718 | 2 |
| #14527278 | 2 |
| #14527108 | 2 |
| C17×#2548 | 2 |
| #18401 | 17 |