Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 25. C42×C53 | C16 | semidirect |
| 45. C4×C53 | C4⋊C16 | semidirect |
| 58. C53 | #12898 | semidirect |
| 76. C42 | #11719908 | semidirect |
| 95. C4 | C4⋊#11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11719908 | 2 |
| C42×C8×C53 | 2 |
| #12898 | 53 |