Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276857 | C2 | semidirect |
| 4. #20272779 | C2 | semidirect |
| 5. #20272771 | C2 | semidirect |
| 7. C8×Q16×C53 | C2 | semidirect |
| 51. Q16×C53 | SD16 | semidirect |
| 91. C8×C53 | SD32 | semidirect |
| 110. C8×Q16 | D53 | semidirect |
| 133. C53 | #12417 | semidirect |
| 162. Q16 | #11719913 | semidirect |
| 202. C8 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276857 | 2 |
| #20276755 | 2 |
| #20274307 | 2 |
| #20272779 | 2 |
| #20272771 | 2 |
| #20272760 | 2 |
| C8×Q16×C53 | 2 |
| #12417 | 53 |