Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20276648 | C2 | semidirect |
| 3. #20275983 | C2 | semidirect |
| 4. #20272733 | C2 | semidirect |
| 6. #20272657 | C2 | semidirect |
| 186. C53 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276648 | 2 |
| #20276631 | 2 |
| #20275983 | 2 |
| #20272733 | 2 |
| #20272730 | 2 |
| #20272657 | 2 |
| C53×#3262 | 2 |
| #12169 | 53 |