Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #20277077 | C2 | semidirect |
| 3. #20275635 | C2 | semidirect |
| 4. #20273157 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1505 | C2 | semidirect |
| 11. #16810910 | C4 | semidirect |
| 12. #16810815 | C4 | semidirect |
| 46. C4⋊#88322 | C2×C4 | semidirect |
| 57. C4⋊Q8×C53 | C2×C4 | semidirect |
| 58. #127×C53 | C2×C4 | semidirect |
| 158. D212 | #104 | semidirect |
| 193. #1505 | D53 | semidirect |
| 225. C53 | #9325 | semidirect |
| 232. C4⋊Q8 | C4×D53 | semidirect |
| 233. #127 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284802 | 2 |
| #20277077 | 2 |
| #20275635 | 2 |
| #20273157 | 2 |
| #20272608 | 2 |
| #20272570 | 2 |
| C53×#1505 | 2 |
| #9325 | 53 |