Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 99 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×D272 | C2 | semidirect |
| 2. C2×#11763080 | C2 | semidirect |
| 3. #14538433 | C2 | semidirect |
| 4. C2×#11762621 | C2 | semidirect |
| 5. #14530499 | C2 | semidirect |
| 6. C2×#11762592 | C2 | semidirect |
| 7. C17×#1382 | C2 | semidirect |
| 50. C2×D136 | D4 | semidirect |
| 64. C2×C16×C17 | D4 | semidirect |
| 66. C17×#108 | D4 | semidirect |
| 179. #1382 | D17 | semidirect |
| 267. C2×C16 | D68 | semidirect |
| 269. #108 | D68 | semidirect |
| 274. C17 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| C2×#11763080 | 2 |
| #14538433 | 2 |
| C2×#11762621 | 2 |
| #14530499 | 2 |
| C2×#11762592 | 2 |
| C17×#1382 | 2 |
| #13319 | 17 |