Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
690 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 136 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. C4×C22⋊#88324 | C2 | semidirect |
| 2. #20289535 | C2 | semidirect |
| 3. #20289531 | C2 | semidirect |
| 37. C2×#41×C53 | C8 | semidirect |
| 175. C53 | #7563 | semidirect |
| 179. C2×#41 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#88324 | 2 |
| #20289535 | 2 |
| #20289531 | 2 |
| #20277206 | 2 |
| #7563 | 53 |