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×#11763240 | C2 | semidirect |
| 2. #14539213 | C2 | semidirect |
| 3. #14539211 | C2 | semidirect |
| 4. #14531044 | C2 | semidirect |
| 5. #14531040 | C2 | semidirect |
| 6. #14531036 | C2 | semidirect |
| 7. #14531033 | C2 | semidirect |
| 8. C4×C16×D17 | C2 | semidirect |
| 9. C17×#2248 | C2 | semidirect |
| 77. C16×D17 | D4 | semidirect |
| 157. #2248 | D17 | semidirect |
| 169. C4×C17 | #508 | semidirect |
| 248. C17 | #33713 | semidirect |
| 333. C4 | #11763240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763240 | 2 |
| #14539213 | 2 |
| #14539211 | 2 |
| #14531044 | 2 |
| #14531040 | 2 |
| #14531036 | 2 |
| #14531033 | 2 |
| C4×C16×D17 | 2 |
| C17×#2248 | 2 |
| #33713 | 17 |