Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20276293 | C2 | semidirect |
| 2. #20275889 | C2 | semidirect |
| 3. #20275885 | C2 | semidirect |
| 4. #20275694 | C2 | semidirect |
| 7. #20274955 | C2 | semidirect |
| 8. #20274953 | C2 | semidirect |
| 56. C4⋊Q8×C53 | Q8 | semidirect |
| 57. #127×C53 | Q8 | semidirect |
| 58. #124×C53 | Q8 | semidirect |
| 59. #124×C53 | Q8 | semidirect |
| 200. C53 | #32705 | semidirect |
| 211. C4⋊Q8 | Dic106 | semidirect |
| 212. #127 | Dic106 | semidirect |
| 214. #124 | Dic106 | semidirect |
| 215. #124 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276293 | 2 |
| #20275889 | 2 |
| #20275885 | 2 |
| #20275694 | 2 |
| #20275548 | 2 |
| #20275099 | 2 |
| #20274955 | 2 |
| #20274953 | 2 |
| C53×#1884 | 2 |
| #32705 | 53 |