Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
696 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16811052 | C2 | semidirect |
| 2. #20286473 | C2 | semidirect |
| 3. #20276798 | C2 | semidirect |
| 4. #20276752 | C2 | semidirect |
| 5. #20276635 | C2 | semidirect |
| 6. C4×Dic424 | C2 | semidirect |
| 7. C16×D212 | C2 | semidirect |
| 8. C53×#2246 | C2 | semidirect |
| 41. Dic424 | D4 | semidirect |
| 123. C4×C53 | #508 | semidirect |
| 131. #2246 | D53 | semidirect |
| 162. C53 | #33853 | semidirect |
| 259. C4 | #16811052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811052 | 2 |
| #20286473 | 2 |
| #20276798 | 2 |
| #20276752 | 2 |
| #20276635 | 2 |
| C4×Dic424 | 2 |
| C16×D212 | 2 |
| C53×#2246 | 2 |
| #33853 | 53 |