Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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. #21422303 | C2 | semidirect |
| 4. #21422302 | C2 | semidirect |
| 5. #21422289 | C2 | semidirect |
| 7. C59×#1420 | C2 | semidirect |
| 82. #1420 | D59 | semidirect |
| 98. C59 | #13718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426201 | 2 |
| #21425889 | 2 |
| #21422303 | 2 |
| #21422302 | 2 |
| #21422289 | 2 |
| #21422235 | 2 |
| C59×#1420 | 2 |
| #13718 | 59 |