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. #20273383 | C2 | semidirect |
| 4. #20273027 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 49. C4⋊#88322 | D4 | semidirect |
| 68. C4⋊C8×C53 | D4 | semidirect |
| 213. #1545 | D53 | semidirect |
| 245. C53 | #9198 | semidirect |
| 278. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283352 | 2 |
| #20280466 | 2 |
| #20273383 | 2 |
| #20273027 | 2 |
| #20272575 | 2 |
| #20272574 | 2 |
| C53×#1545 | 2 |
| #9198 | 53 |