Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
664 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×Q32×D53 | C2 | semidirect |
| 3. #20276803 | C2 | semidirect |
| 4. #20276762 | C2 | semidirect |
| 5. #20276647 | C2 | semidirect |
| 6. C4×Dic424 | C2 | semidirect |
| 8. C53×#2247 | C2 | semidirect |
| 41. Dic424 | D4 | semidirect |
| 100. D212 | Q32 | semidirect |
| 115. C2×D53 | C2×Q32 | semidirect |
| 118. C4×C53 | C2×Q32 | semidirect |
| 126. #2247 | D53 | semidirect |
| 156. C53 | D4×Q32 | semidirect |
| 248. C4 | Q32×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D53 | 2 |
| #20286465 | 2 |
| #20276803 | 2 |
| #20276762 | 2 |
| #20276647 | 2 |
| C4×Dic424 | 2 |
| C16×D212 | 2 |
| C53×#2247 | 2 |
| D4×Q32 | 53 |