Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20285640 | C2 | semidirect |
| 3. #20273396 | C2 | semidirect |
| 4. #20273209 | C2 | semidirect |
| 5. #20273106 | C2 | semidirect |
| 6. #20272618 | C2 | semidirect |
| 7. C53×#2542 | C2 | semidirect |
| 87. C2×D4×C53 | SD16 | semidirect |
| 212. #2542 | D53 | semidirect |
| 247. C53 | #10240 | semidirect |
| 313. C2×D4 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285640 | 2 |
| #20284179 | 2 |
| #20273396 | 2 |
| #20273209 | 2 |
| #20273106 | 2 |
| #20272618 | 2 |
| C53×#2542 | 2 |
| #10240 | 53 |