Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20283352 | C2 | semidirect |
| 3. #20273384 | C2 | semidirect |
| 4. #20273382 | C2 | semidirect |
| 5. #20273027 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 55. C4⋊#88322 | D4 | semidirect |
| 66. C4⋊C8×C53 | D4 | semidirect |
| 216. #1286 | D53 | semidirect |
| 245. C53 | #9198 | semidirect |
| 278. C4⋊C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283352 | 2 |
| #20280468 | 2 |
| #20273384 | 2 |
| #20273382 | 2 |
| #20273027 | 2 |
| #20272573 | 2 |
| C53×#1286 | 2 |
| #9198 | 53 |