Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #20272767 | C2 | semidirect |
| 5. #20272697 | C2 | semidirect |
| 6. #20272685 | C2 | semidirect |
| 7. C53×#3390 | C2 | semidirect |
| 68. Q16×C53 | SD16 | semidirect |
| 136. #3390 | D53 | semidirect |
| 166. C53 | #12361 | semidirect |
| 208. Q16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276958 | 2 |
| #20276755 | 2 |
| #20274199 | 2 |
| #20272767 | 2 |
| #20272697 | 2 |
| #20272685 | 2 |
| C53×#3390 | 2 |
| #12361 | 53 |