Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 17. C4⋊Q8×C53 | C8 | semidirect |
| 110. C53 | #7605 | semidirect |
| 114. C4⋊Q8 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274858 | 2 |
| #20272541 | 2 |
| C4×C4⋊Q8×C53 | 2 |
| #7605 | 53 |