Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #20289745 | C2 | semidirect |
| 4. #20289744 | C2 | semidirect |
| 5. #20289738 | C2 | semidirect |
| 6. #20289737 | C2 | semidirect |
| 63. #11719912 | C16 | semidirect |
| 87. C8×C53 | C2×C16 | semidirect |
| 91. #88322 | C2×C16 | semidirect |
| 133. C53 | #12015 | semidirect |
| 204. C8 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291075 | 2 |
| D53⋊(C4⋊C16) | 2 |
| #20289745 | 2 |
| #20289744 | 2 |
| #20289738 | 2 |
| #20289737 | 2 |
| #20272994 | 2 |
| #12015 | 53 |