Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
400 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276964 | C2 | semidirect |
| 2. #20276755 | C2 | semidirect |
| 3. #20274070 | C2 | semidirect |
| 4. #20272761 | C2 | semidirect |
| 5. #20272679 | C2 | semidirect |
| 6. D4⋊#11719908 | C2 | semidirect |
| 7. C53×#3287 | C2 | semidirect |
| 71. Q16×C53 | D8 | semidirect |
| 147. #3287 | D53 | semidirect |
| 177. C53 | #12317 | semidirect |
| 224. Q16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276964 | 2 |
| #20276755 | 2 |
| #20274070 | 2 |
| #20272761 | 2 |
| #20272679 | 2 |
| D4⋊#11719908 | 2 |
| C53×#3287 | 2 |
| #12317 | 53 |