Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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×D136 | C2 | semidirect |
| 2. #14531007 | C2 | semidirect |
| 4. #14526840 | C2 | semidirect |
| 5. Q8⋊#63214 | C2 | semidirect |
| 6. #14526744 | C2 | semidirect |
| 7. C17×#1668 | C2 | semidirect |
| 83. D136 | SD16 | semidirect |
| 90. Q8×C17 | D16 | semidirect |
| 119. #1668 | D17 | semidirect |
| 189. C17 | #12352 | semidirect |
| 229. Q8 | #10587497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D136 | 2 |
| #14531007 | 2 |
| #14530816 | 2 |
| #14526840 | 2 |
| Q8⋊#63214 | 2 |
| #14526744 | 2 |
| C17×#1668 | 2 |
| #12352 | 17 |