Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1078 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21435087 | C2 | semidirect |
| 3. #21423400 | C2 | semidirect |
| 4. #21423384 | C2 | semidirect |
| 5. #21422731 | C2 | semidirect |
| 6. #21422706 | C2 | semidirect |
| 7. C59×#3150 | C2 | semidirect |
| 16. #16837789 | C22 | semidirect |
| 17. #16837764 | C22 | semidirect |
| 21. #16837459 | C22 | semidirect |
| 22. #16837142 | C22 | semidirect |
| 23. #16837141 | C22 | semidirect |
| 26. C59×#532 | C22 | semidirect |
| 28. C59×#497 | C22 | semidirect |
| 30. C59×#496 | C22 | semidirect |
| 31. C2×#97×C59 | C22 | semidirect |
| 187. #3150 | D59 | semidirect |
| 208. #532 | C2×D59 | semidirect |
| 210. #497 | C2×D59 | semidirect |
| 213. #496 | C2×D59 | semidirect |
| 219. C2×#97 | C2×D59 | semidirect |
| 222. C59 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438501 | 2 |
| #21435087 | 2 |
| #21423400 | 2 |
| #21423384 | 2 |
| #21422731 | 2 |
| #21422706 | 2 |
| C59×#3150 | 2 |
| #19052 | 59 |