Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #14539704 | C2 | semidirect |
| 2. #14538248 | C2 | semidirect |
| 3. #14533730 | C2 | semidirect |
| 4. #14527451 | C2 | semidirect |
| 5. #14527280 | C2 | semidirect |
| 6. #14526686 | C2 | semidirect |
| 7. C17×#1478 | C2 | semidirect |
| 64. #10587560 | D4 | semidirect |
| 67. #10587555 | D4 | semidirect |
| 69. C17×C4⋊C8 | D4 | semidirect |
| 79. C4⋊#3622 | D4 | semidirect |
| 87. C2×D4×C17 | D8 | semidirect |
| 209. #1478 | D17 | semidirect |
| 311. C4⋊C8 | C22⋊D17 | semidirect |
| 320. C17 | #10238 | semidirect |
| 352. C2×D4 | D136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539704 | 2 |
| #14538248 | 2 |
| #14533730 | 2 |
| #14527451 | 2 |
| #14527280 | 2 |
| #14526686 | 2 |
| C17×#1478 | 2 |
| #10238 | 17 |