Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276982 | C2 | semidirect |
| 2. #20276755 | C2 | semidirect |
| 3. #20274194 | C2 | semidirect |
| 4. #20272758 | C2 | semidirect |
| 5. #20272685 | C2 | semidirect |
| 6. #20272673 | C2 | semidirect |
| 7. C53×#3277 | C2 | semidirect |
| 85. Q16×C53 | D8 | semidirect |
| 167. #3277 | D53 | semidirect |
| 199. C53 | #12325 | semidirect |
| 258. Q16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276982 | 2 |
| #20276755 | 2 |
| #20274194 | 2 |
| #20272758 | 2 |
| #20272685 | 2 |
| #20272673 | 2 |
| C53×#3277 | 2 |
| #12325 | 53 |