Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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. #364×D53 | C2 | semidirect |
| 3. #20273000 | C2 | semidirect |
| 4. #20272692 | C2 | semidirect |
| 5. #20272691 | C2 | semidirect |
| 6. #20272690 | C2 | semidirect |
| 7. C53×#1336 | C2 | semidirect |
| 20. #16810444 | C22 | semidirect |
| 22. #16810344 | C22 | semidirect |
| 25. C53×#364 | C22 | semidirect |
| 26. C53×#322 | C22 | semidirect |
| 28. #13133240 | C8 | semidirect |
| 32. #13133236 | C8 | semidirect |
| 33. Q16×D53 | C8 | semidirect |
| 35. D8×D53 | C8 | semidirect |
| 181. #1336 | D53 | semidirect |
| 203. #364 | C2×D53 | semidirect |
| 205. #322 | C2×D53 | semidirect |
| 207. C53 | #11604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #443×D53 | 2 |
| #364×D53 | 2 |
| #20273000 | 2 |
| #20272692 | 2 |
| #20272691 | 2 |
| #20272690 | 2 |
| C53×#1336 | 2 |
| #11604 | 53 |