Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #20273489 | C2 | semidirect |
| 4. #20273279 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1542 | C2 | semidirect |
| 170. #1542 | D53 | semidirect |
| 199. C53 | #10469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284508 | 2 |
| #20274726 | 2 |
| #20273489 | 2 |
| #20273279 | 2 |
| #20273035 | 2 |
| #20272574 | 2 |
| C53×#1542 | 2 |
| #10469 | 53 |