Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1154 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 2. #20284747 | C2 | semidirect |
| 3. #20280077 | C2 | semidirect |
| 4. #20273754 | C2 | semidirect |
| 5. #20273686 | C2 | semidirect |
| 6. #20273276 | C2 | semidirect |
| 7. C53×#1461 | C2 | semidirect |
| 84. C2×Q8×C53 | SD16 | semidirect |
| 195. #1461 | D53 | semidirect |
| 226. C53 | #18219 | semidirect |
| 289. C2×Q8 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20284747 | 2 |
| #20280077 | 2 |
| #20273754 | 2 |
| #20273686 | 2 |
| #20273276 | 2 |
| C53×#1461 | 2 |
| #18219 | 53 |