Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 306 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. #20276915 | C2 | semidirect |
| 2. #20276910 | C2 | semidirect |
| 4. #20272733 | C2 | semidirect |
| 5. #20272733 | C2 | semidirect |
| 177. C53 | #12286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276915 | 2 |
| #20276910 | 2 |
| #20276155 | 2 |
| #20272733 | 2 |
| #20272641 | 2 |
| C53×#3202 | 2 |
| #12286 | 53 |