Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1318 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. #20275858 | C2 | semidirect |
| 4. #20275798 | C2 | semidirect |
| 5. #20275070 | C2 | semidirect |
| 6. #20275028 | C2 | semidirect |
| 7. #20274786 | C2 | semidirect |
| 8. C2×C53×#541 | C2 | semidirect |
| 13. C2×#13133141 | C22 | semidirect |
| 20. #16810385 | C22 | semidirect |
| 21. #16810378 | C22 | semidirect |
| 22. #16810378 | C22 | semidirect |
| 24. C2×C4⋊Q8×C53 | C22 | semidirect |
| 27. C2×#125×C53 | C22 | semidirect |
| 29. C2×C4×Q8×C53 | C22 | semidirect |
| 181. C2×#541 | D53 | semidirect |
| 198. C2×C4⋊Q8 | C2×D53 | semidirect |
| 201. C2×#125 | C2×D53 | semidirect |
| 203. C2×C4×Q8 | C2×D53 | semidirect |
| 217. C53 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810773 | 2 |
| #20277295 | 2 |
| #20275858 | 2 |
| #20275798 | 2 |
| #20275070 | 2 |
| #20275028 | 2 |
| #20274786 | 2 |
| C2×C53×#541 | 2 |
| #23942 | 53 |