Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20275554 | C2 | semidirect |
| 3. #20273506 | C2 | semidirect |
| 4. #20273384 | C2 | semidirect |
| 5. #20273132 | C2 | semidirect |
| 6. #20272604 | C2 | semidirect |
| 7. C53×#1560 | C2 | semidirect |
| 170. #1560 | D53 | semidirect |
| 199. C53 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20275554 | 2 |
| #20273506 | 2 |
| #20273384 | 2 |
| #20273132 | 2 |
| #20272604 | 2 |
| C53×#1560 | 2 |
| #10488 | 53 |