Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21433237 | C2 | semidirect |
| 3. #21425024 | C2 | semidirect |
| 4. #21422622 | C2 | semidirect |
| 5. #21421965 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1555 | C2 | semidirect |
| 9. #16837789 | C4 | semidirect |
| 10. #16837766 | C4 | semidirect |
| 212. #1555 | D59 | semidirect |
| 248. C59 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435114 | 2 |
| #21433237 | 2 |
| #21425024 | 2 |
| #21422622 | 2 |
| #21421965 | 2 |
| #21421953 | 2 |
| C59×#1555 | 2 |
| #9378 | 59 |