Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21425767 | C2 | semidirect |
| 3. #21424641 | C2 | semidirect |
| 4. #21424624 | C2 | semidirect |
| 5. #21424384 | C2 | semidirect |
| 6. #21422226 | C2 | semidirect |
| 7. C59×#2122 | C2 | semidirect |
| 197. #2122 | D59 | semidirect |
| 230. C59 | #13432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434957 | 2 |
| #21425767 | 2 |
| #21424641 | 2 |
| #21424624 | 2 |
| #21424384 | 2 |
| #21422226 | 2 |
| C59×#2122 | 2 |
| #13432 | 59 |