Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21434648 | C2 | semidirect |
| 3. #21433919 | C2 | semidirect |
| 4. #21430041 | C2 | semidirect |
| 5. #21425307 | C2 | semidirect |
| 6. #21425076 | C2 | semidirect |
| 7. #21424308 | C2 | semidirect |
| 8. #21423909 | C2 | semidirect |
| 9. C59×#1965 | C2 | semidirect |
| 114. M16×C59 | #41 | semidirect |
| 201. #1965 | D59 | semidirect |
| 236. C59 | #25690 | semidirect |
| 314. M16 | #11745687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437970 | 2 |
| #21434648 | 2 |
| #21433919 | 2 |
| #21430041 | 2 |
| #21425307 | 2 |
| #21425076 | 2 |
| #21424308 | 2 |
| #21423909 | 2 |
| C59×#1965 | 2 |
| #25690 | 59 |