Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20273425 | C2 | semidirect |
| 3. #20273344 | C2 | semidirect |
| 4. #20273290 | C2 | semidirect |
| 5. #20273261 | C2 | semidirect |
| 6. #20273183 | C2 | semidirect |
| 7. C53×#1515 | C2 | semidirect |
| 10. #16811358 | C4 | semidirect |
| 11. #16811351 | C4 | semidirect |
| 13. #16811295 | C4 | semidirect |
| 14. Q8×D212 | C4 | semidirect |
| 263. #1515 | D53 | semidirect |
| 303. C53 | #8503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289186 | 2 |
| #20273425 | 2 |
| #20273344 | 2 |
| #20273290 | 2 |
| #20273261 | 2 |
| #20273183 | 2 |
| C53×#1515 | 2 |
| #8503 | 53 |