Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
726 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 140 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. #20290843 | C2 | semidirect |
| 2. #20290651 | C2 | semidirect |
| 3. C8×D53⋊C8 | C2 | semidirect |
| 12. #16811000 | C4 | semidirect |
| 13. #16810999 | C4 | semidirect |
| 16. C53×#493 | C4 | semidirect |
| 58. D53⋊C8 | D8 | semidirect |
| 93. C8×C53 | #102 | semidirect |
| 94. #88322 | #102 | semidirect |
| 129. #493 | #6157 | semidirect |
| 136. C53 | #9824 | semidirect |
| 214. C8 | #13133279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290843 | 2 |
| #20290651 | 2 |
| C8×D53⋊C8 | 2 |
| #493×D53 | 2 |
| #9824 | 53 |