Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 94 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. Q8×#63243 | C2 | semidirect |
| 3. C4×#10587549 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543615 | C2 | semidirect |
| 25. #11763095 | C4 | semidirect |
| 26. #11763094 | C4 | semidirect |
| 27. #11763006 | C4 | semidirect |
| 32. C17×#460 | C4 | semidirect |
| 118. #63243 | SD16 | semidirect |
| 151. Q8×C17 | #104 | semidirect |
| 228. #460 | #595 | semidirect |
| 304. C17 | #8992 | semidirect |
| 373. Q8 | #10587548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63243 | 2 |
| #14544948 | 2 |
| C4×#10587549 | 2 |
| #14544130 | 2 |
| #14543681 | 2 |
| #14543615 | 2 |
| #14538814 | 2 |
| #8992 | 17 |