Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20285706 | C2 | semidirect |
| 2. #20285702 | C2 | semidirect |
| 3. #20273184 | C2 | semidirect |
| 4. #20273133 | C2 | semidirect |
| 5. #20273067 | C2 | semidirect |
| 6. #20272587 | C2 | semidirect |
| 7. C53×#3153 | C2 | semidirect |
| 208. #3153 | D53 | semidirect |
| 245. C53 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285706 | 2 |
| #20285702 | 2 |
| #20273184 | 2 |
| #20273133 | 2 |
| #20273067 | 2 |
| #20272587 | 2 |
| C53×#3153 | 2 |
| #10120 | 53 |