Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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. D53⋊#364 | C2 | semidirect |
| 3. #20290651 | C2 | semidirect |
| 4. #20289791 | C2 | semidirect |
| 16. #16810741 | C4 | semidirect |
| 17. #16810740 | C4 | semidirect |
| 18. #16810739 | C4 | semidirect |
| 24. C53×#443 | C4 | semidirect |
| 83. Q16×C53 | C4⋊C4 | semidirect |
| 85. D8×C53 | C4⋊C4 | semidirect |
| 103. Dic212 | C4⋊C4 | semidirect |
| 104. D424 | C4⋊C4 | semidirect |
| 199. #443 | #6157 | semidirect |
| 210. C53 | #12821 | semidirect |
| 268. Q16 | C4⋊#6157 | semidirect |
| 275. D8 | C4⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#364 | 2 |
| #20291023 | 2 |
| #20290651 | 2 |
| #20289791 | 2 |
| #443×D53 | 2 |
| #12821 | 53 |