Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #21422863 | C2 | semidirect |
| 4. #21422826 | C2 | semidirect |
| 6. #21421968 | C2 | semidirect |
| 7. C59×#1526 | C2 | semidirect |
| 181. #1526 | D59 | semidirect |
| 211. C59 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435095 | 2 |
| #21424945 | 2 |
| #21422863 | 2 |
| #21422826 | 2 |
| #21422693 | 2 |
| #21421968 | 2 |
| C59×#1526 | 2 |
| #10498 | 59 |