Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276942 | C2 | semidirect |
| 2. #20276857 | C2 | semidirect |
| 4. #20272764 | C2 | semidirect |
| 5. #20272679 | C2 | semidirect |
| 68. Q16×C53 | SD16 | semidirect |
| 159. C53 | #12370 | semidirect |
| 203. Q16 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276942 | 2 |
| #20276857 | 2 |
| #20274104 | 2 |
| #20272764 | 2 |
| #20272679 | 2 |
| D4⋊#11719908 | 2 |
| D4×Q16×C53 | 2 |
| #12370 | 53 |