Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20275536 | C2 | semidirect |
| 4. #20273279 | C2 | semidirect |
| 6. #20272559 | C2 | semidirect |
| 7. C53×#3229 | C2 | semidirect |
| 176. #3229 | D53 | semidirect |
| 212. C53 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285836 | 2 |
| #20285063 | 2 |
| #20275536 | 2 |
| #20273279 | 2 |
| #20273276 | 2 |
| #20272559 | 2 |
| C53×#3229 | 2 |
| #10226 | 53 |