Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
588 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20282708 | C2 | semidirect |
| 3. #20272541 | C2 | semidirect |
| 4. #20272540 | C2 | semidirect |
| 50. C2×Q8×C53 | SD16 | semidirect |
| 74. C2×Dic106 | SD16 | semidirect |
| 172. C53 | #7749 | semidirect |
| 210. C2×Q8 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282708 | 2 |
| #20275803 | 2 |
| #20272541 | 2 |
| #20272540 | 2 |
| C53×#2014 | 2 |
| #7749 | 53 |