Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14539771 | C2 | semidirect |
| 2. #14539236 | C2 | semidirect |
| 3. #14534892 | C2 | semidirect |
| 4. #14527497 | C2 | semidirect |
| 5. #14527293 | C2 | semidirect |
| 6. #14526678 | C2 | semidirect |
| 7. C17×#1527 | C2 | semidirect |
| 62. #10587560 | D4 | semidirect |
| 65. #10587555 | D4 | semidirect |
| 69. C17×#97 | D4 | semidirect |
| 76. C4⋊#3622 | D4 | semidirect |
| 184. #1527 | D17 | semidirect |
| 285. #97 | C22⋊D17 | semidirect |
| 289. C17 | #10088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539771 | 2 |
| #14539236 | 2 |
| #14534892 | 2 |
| #14527497 | 2 |
| #14527293 | 2 |
| #14526678 | 2 |
| C17×#1527 | 2 |
| #10088 | 17 |