Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
602 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 602 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. #20283755 | C2 | semidirect |
| 3. #20274704 | C2 | semidirect |
| 4. #20273140 | C2 | semidirect |
| 5. #20272575 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1486 | C2 | semidirect |
| 49. C4×#88322 | D4 | semidirect |
| 67. C4×C8×C53 | D4 | semidirect |
| 207. #1486 | D53 | semidirect |
| 236. C53 | #9489 | semidirect |
| 274. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283755 | 2 |
| #20279616 | 2 |
| #20274704 | 2 |
| #20273140 | 2 |
| #20272575 | 2 |
| #20272574 | 2 |
| C53×#1486 | 2 |
| #9489 | 53 |