Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
468 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. #14544497 | C2 | semidirect |
| 4. #14543986 | C2 | semidirect |
| 5. #14543616 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 8. #11763859 | C4 | semidirect |
| 9. #11763844 | C4 | semidirect |
| 25. #11762541 | C4 | semidirect |
| 26. #11762539 | C4 | semidirect |
| 27. D4⋊#3622 | C4 | semidirect |
| 28. C17×D4⋊C8 | C4 | semidirect |
| 89. #63243 | M16 | semidirect |
| 191. D4⋊C8 | #595 | semidirect |
| 236. C17 | #8197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545596 | 2 |
| C4×#10587548 | 2 |
| #14544497 | 2 |
| #14543986 | 2 |
| #14543616 | 2 |
| #14543611 | 2 |
| #14527163 | 2 |
| #8197 | 17 |