Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20285698 | C2 | semidirect |
| 2. #20285168 | C2 | semidirect |
| 3. #20280821 | C2 | semidirect |
| 4. #20273428 | C2 | semidirect |
| 5. #20273314 | C2 | semidirect |
| 6. #20272608 | C2 | semidirect |
| 7. C53×#1505 | C2 | semidirect |
| 56. C4⋊#88322 | D4 | semidirect |
| 61. #13133128 | D4 | semidirect |
| 64. C4⋊Q8×C53 | D4 | semidirect |
| 65. #127×C53 | D4 | semidirect |
| 210. #1505 | D53 | semidirect |
| 242. C53 | #10088 | semidirect |
| 256. C4⋊Q8 | D212 | semidirect |
| 262. #127 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285698 | 2 |
| #20285168 | 2 |
| #20280821 | 2 |
| #20273428 | 2 |
| #20273314 | 2 |
| #20272608 | 2 |
| C53×#1505 | 2 |
| #10088 | 53 |