Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21422569 | C2 | semidirect |
| 5. #21422452 | C2 | semidirect |
| 6. #21421968 | C2 | semidirect |
| 7. C59×#3166 | C2 | semidirect |
| 179. #3166 | D59 | semidirect |
| 214. C59 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435286 | 2 |
| #21435103 | 2 |
| #21422569 | 2 |
| #21422514 | 2 |
| #21422452 | 2 |
| #21421968 | 2 |
| C59×#3166 | 2 |
| #10126 | 59 |