Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#10587499 | C2 | semidirect |
| 3. C2×#11762621 | C2 | semidirect |
| 4. #14530504 | C2 | semidirect |
| 5. C2×#11762593 | C2 | semidirect |
| 6. #14526881 | C2 | semidirect |
| 7. C2×C17×#473 | C2 | semidirect |
| 40. C2×Q16×C17 | D4 | semidirect |
| 63. C17×#108 | D4 | semidirect |
| 74. C2×#63214 | D4 | semidirect |
| 173. C2×#473 | D17 | semidirect |
| 234. C2×Q16 | C22⋊D17 | semidirect |
| 264. #108 | C22⋊D17 | semidirect |
| 269. C17 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587499 | 2 |
| #14538432 | 2 |
| C2×#11762621 | 2 |
| #14530504 | 2 |
| C2×#11762593 | 2 |
| #14526881 | 2 |
| C2×C17×#473 | 2 |
| #13321 | 17 |