Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. C4⋊C16×D53 | C2 | semidirect |
| 3. #20273475 | C2 | semidirect |
| 4. #20272767 | C2 | semidirect |
| 5. #20272759 | C2 | semidirect |
| 6. #20272757 | C2 | semidirect |
| 7. C53×#1363 | C2 | semidirect |
| 149. #1363 | D53 | semidirect |
| 176. C53 | #11978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285287 | 2 |
| C4⋊C16×D53 | 2 |
| #20273475 | 2 |
| #20272767 | 2 |
| #20272759 | 2 |
| #20272757 | 2 |
| C53×#1363 | 2 |
| #11978 | 53 |