Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
488 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21433232 | C2 | semidirect |
| 3. #21422682 | C2 | semidirect |
| 4. #21422539 | C2 | semidirect |
| 5. #21421995 | C2 | semidirect |
| 6. #21421946 | C2 | semidirect |
| 7. C59×#1955 | C2 | semidirect |
| 223. #1955 | D59 | semidirect |
| 262. C59 | #9052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434143 | 2 |
| #21433232 | 2 |
| #21422682 | 2 |
| #21422539 | 2 |
| #21421995 | 2 |
| #21421946 | 2 |
| C59×#1955 | 2 |
| #9052 | 59 |