Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
442 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #21432088 | C2 | semidirect |
| 4. #21422127 | C2 | semidirect |
| 5. #21422126 | C2 | semidirect |
| 6. #21422029 | C2 | semidirect |
| 94. C2×Dic118 | SD16 | semidirect |
| 216. C59 | #12130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432088 | 2 |
| #21425143 | 2 |
| #21423065 | 2 |
| #21422127 | 2 |
| #21422126 | 2 |
| #21422029 | 2 |
| C59×#1604 | 2 |
| #12130 | 59 |