Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1132 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 163 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. #21438501 | C2 | semidirect |
| 2. #21435014 | C2 | semidirect |
| 3. #21423177 | C2 | semidirect |
| 4. #21423148 | C2 | semidirect |
| 5. #21422758 | C2 | semidirect |
| 6. #21422514 | C2 | semidirect |
| 7. C59×#3151 | C2 | semidirect |
| 9. #16838118 | C22 | semidirect |
| 12. #16838037 | C22 | semidirect |
| 18. #16837594 | C22 | semidirect |
| 20. #16837455 | C22 | semidirect |
| 21. #16837151 | C22 | semidirect |
| 22. #16837146 | C22 | semidirect |
| 23. #16837131 | C22 | semidirect |
| 26. C2×#127×C59 | C22 | semidirect |
| 29. C59×#492 | C22 | semidirect |
| 30. C4×M16×C59 | C22 | semidirect |
| 176. #3151 | D59 | semidirect |
| 197. C2×#127 | C2×D59 | semidirect |
| 201. #492 | C2×D59 | semidirect |
| 206. C4×M16 | C2×D59 | semidirect |
| 210. C59 | #18714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438501 | 2 |
| #21435014 | 2 |
| #21423177 | 2 |
| #21423148 | 2 |
| #21422758 | 2 |
| #21422514 | 2 |
| C59×#3151 | 2 |
| #18714 | 59 |