Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #20273397 | C2 | semidirect |
| 5. #20273386 | C2 | semidirect |
| 6. #20272605 | C2 | semidirect |
| 7. C53×#1299 | C2 | semidirect |
| 171. #1299 | D53 | semidirect |
| 199. C53 | #9433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285109 | 2 |
| #20283781 | 2 |
| #20273448 | 2 |
| #20273397 | 2 |
| #20273386 | 2 |
| #20272605 | 2 |
| C53×#1299 | 2 |
| #9433 | 53 |