Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20276517 | C2 | semidirect |
| 3. #346×D53 | C2 | semidirect |
| 4. #20272697 | C2 | semidirect |
| 5. #20272674 | C2 | semidirect |
| 6. #20272672 | C2 | semidirect |
| 7. C53×#1338 | C2 | semidirect |
| 152. #1338 | D53 | semidirect |
| 179. C53 | #11619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283680 | 2 |
| #20276517 | 2 |
| #346×D53 | 2 |
| #20272697 | 2 |
| #20272674 | 2 |
| #20272672 | 2 |
| C53×#1338 | 2 |
| #11619 | 53 |