Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 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×#16811056 | C2 | semidirect |
| 2. #20286474 | C2 | semidirect |
| 3. #20276965 | C2 | semidirect |
| 4. #20276802 | C2 | semidirect |
| 5. #20276755 | C2 | semidirect |
| 6. #20276641 | C2 | semidirect |
| 7. C16×D212 | C2 | semidirect |
| 8. C4×Q32×C53 | C2 | semidirect |
| 52. Q32×C53 | D4 | semidirect |
| 125. C4×C53 | #508 | semidirect |
| 135. C4×Q32 | D53 | semidirect |
| 162. C53 | #33853 | semidirect |
| 178. Q32 | D212 | semidirect |
| 259. C4 | #16811056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811056 | 2 |
| #20286474 | 2 |
| #20276965 | 2 |
| #20276802 | 2 |
| #20276755 | 2 |
| #20276641 | 2 |
| C16×D212 | 2 |
| C4×Q32×C53 | 2 |
| #33853 | 53 |