Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
954 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
| 2. C2×#16811535 | C2 | semidirect |
| 3. D53⋊(C22⋊C16) | C2 | semidirect |
| 4. #20290592 | C2 | semidirect |
| 15. C2×#13133240 | C4 | semidirect |
| 16. C2×#13133239 | C4 | semidirect |
| 19. C2×#13133236 | C4 | semidirect |
| 26. C2×#135×C53 | C4 | semidirect |
| 127. Q16×C53 | C22⋊C4 | semidirect |
| 130. D8×C53 | C22⋊C4 | semidirect |
| 143. Dic212 | C22⋊C4 | semidirect |
| 145. D424 | C22⋊C4 | semidirect |
| 261. C2×#135 | #6157 | semidirect |
| 274. C53 | #12733 | semidirect |
| 375. Q16 | C22⋊#6157 | semidirect |
| 384. D8 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811536 | 2 |
| C2×#16811535 | 2 |
| D53⋊(C22⋊C16) | 2 |
| #20290592 | 2 |
| C2×#135×D53 | 2 |
| #12733 | 53 |