Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276940 | C2 | semidirect |
| 3. #20274075 | C2 | semidirect |
| 4. #20272770 | C2 | semidirect |
| 5. Q8⋊#11719908 | C2 | semidirect |
| 6. #20272676 | C2 | semidirect |
| 7. Q8×D8×C53 | C2 | semidirect |
| 65. D8×C53 | SD16 | semidirect |
| 92. Q8×C53 | D16 | semidirect |
| 132. Q8×D8 | D53 | semidirect |
| 161. C53 | #12352 | semidirect |
| 206. D8 | #11719924 | semidirect |
| 229. Q8 | #13133158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276940 | 2 |
| #20276750 | 2 |
| #20274075 | 2 |
| #20272770 | 2 |
| Q8⋊#11719908 | 2 |
| #20272676 | 2 |
| Q8×D8×C53 | 2 |
| #12352 | 53 |