Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#11763238 | C2 | semidirect |
| 2. #14539211 | C2 | semidirect |
| 3. #14531042 | C2 | semidirect |
| 4. #14531039 | C2 | semidirect |
| 5. #14531037 | C2 | semidirect |
| 6. C4×C16×D17 | C2 | semidirect |
| 7. C17×#2246 | C2 | semidirect |
| 51. C16×D17 | D4 | semidirect |
| 107. #2246 | D17 | semidirect |
| 114. C4×C17 | #508 | semidirect |
| 168. C17 | #33713 | semidirect |
| 226. C4 | #11763238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763238 | 2 |
| #14539211 | 2 |
| #14531042 | 2 |
| #14531039 | 2 |
| #14531037 | 2 |
| C4×C16×D17 | 2 |
| C17×#2246 | 2 |
| #33713 | 17 |