Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
922 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 195 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. #20285295 | C2 | semidirect |
| 2. #20285144 | C2 | semidirect |
| 3. #20274330 | C2 | semidirect |
| 4. #20274322 | C2 | semidirect |
| 5. #20274308 | C2 | semidirect |
| 6. C82×D53 | C2 | semidirect |
| 7. C53×#1713 | C2 | semidirect |
| 68. C8×D53 | D8 | semidirect |
| 84. C8×C53 | #135 | semidirect |
| 100. #1713 | D53 | semidirect |
| 125. C53 | #19603 | semidirect |
| 188. C8 | #13133240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285295 | 2 |
| #20285144 | 2 |
| #20274330 | 2 |
| #20274322 | 2 |
| #20274308 | 2 |
| C82×D53 | 2 |
| C53×#1713 | 2 |
| #19603 | 53 |