Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20275179 | C2 | semidirect |
| 3. #20275151 | C2 | semidirect |
| 4. #20274922 | C2 | semidirect |
| 5. #20273074 | C2 | semidirect |
| 6. #20272621 | C2 | semidirect |
| 7. C53×#1519 | C2 | semidirect |
| 220. #1519 | D53 | semidirect |
| 253. C53 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285512 | 2 |
| #20275179 | 2 |
| #20275151 | 2 |
| #20274922 | 2 |
| #20273074 | 2 |
| #20272621 | 2 |
| C53×#1519 | 2 |
| #10560 | 53 |