Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 198. C53 | #7836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282677 | 2 |
| #20276254 | 2 |
| #20272540 | 2 |
| #20272538 | 2 |
| C53×#2100 | 2 |
| #7836 | 53 |