Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20286515 | C2 | semidirect |
| 2. #20276788 | C2 | semidirect |
| 3. #20274329 | C2 | semidirect |
| 4. #20272751 | C2 | semidirect |
| 5. #20272688 | C2 | semidirect |
| 6. #20272687 | C2 | semidirect |
| 7. C53×#2213 | C2 | semidirect |
| 17. #16810444 | C22 | semidirect |
| 19. C8×#88322 | C22 | semidirect |
| 21. C53×#493 | C22 | semidirect |
| 23. C53×#364 | C22 | semidirect |
| 69. Q16×C53 | D8 | semidirect |
| 75. D8×C53 | D8 | semidirect |
| 87. Dic212 | D8 | semidirect |
| 93. D424 | D8 | semidirect |
| 145. #2213 | D53 | semidirect |
| 162. #493 | C2×D53 | semidirect |
| 169. #364 | C2×D53 | semidirect |
| 173. C53 | #12310 | semidirect |
| 219. Q16 | #11719922 | semidirect |
| 236. D8 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286515 | 2 |
| #20276788 | 2 |
| #20274329 | 2 |
| #20272751 | 2 |
| #20272688 | 2 |
| #20272687 | 2 |
| C53×#2213 | 2 |
| #12310 | 53 |