Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
934 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×#16811536 | C2 | semidirect |
| 13. C22×Dic212 | C4 | semidirect |
| 18. C2×Q16×D53 | C4 | semidirect |
| 21. C22×Q16×C53 | C4 | semidirect |
| 98. Q16×C53 | C22⋊C4 | semidirect |
| 109. Dic212 | C22⋊C4 | semidirect |
| 159. C22×C53 | #358 | semidirect |
| 165. C2×D53 | #358 | semidirect |
| 197. C22×Q16 | #6157 | semidirect |
| 206. C53 | #12732 | semidirect |
| 285. Q16 | C22⋊#6157 | semidirect |
| 352. C22 | #16811536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811536 | 2 |
| D53⋊(C22⋊C16) | 2 |
| #20290592 | 2 |
| C22×Q16×D53 | 2 |
| #12732 | 53 |