Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21432049 | C2 | semidirect |
| 4. #21421921 | C2 | semidirect |
| 5. #21421919 | C2 | semidirect |
| 6. #21421918 | C2 | semidirect |
| 102. C4⋊C4×C59 | SD16 | semidirect |
| 236. C59 | #7747 | semidirect |
| 327. C4⋊C4 | #11745670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432049 | 2 |
| #21425327 | 2 |
| #21425184 | 2 |
| #21421921 | 2 |
| #21421919 | 2 |
| #21421918 | 2 |
| C59×#2041 | 2 |
| #7747 | 59 |