Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
958 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 3. #20273723 | C2 | semidirect |
| 5. #20273279 | C2 | semidirect |
| 6. #20273039 | C2 | semidirect |
| 7. C53×#3502 | C2 | semidirect |
| 86. C2×Q8×C53 | SD16 | semidirect |
| 188. #3502 | D53 | semidirect |
| 225. C53 | #18220 | semidirect |
| 280. C2×Q8 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284719 | 2 |
| #20279620 | 2 |
| #20273723 | 2 |
| #20273655 | 2 |
| #20273279 | 2 |
| #20273039 | 2 |
| C53×#3502 | 2 |
| #18220 | 53 |