Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426346 | C2 | semidirect |
| 2. #21426172 | C2 | semidirect |
| 3. #21422172 | C2 | semidirect |
| 4. #21422132 | C2 | semidirect |
| 5. C59×#2170 | C2 | semidirect |
| 83. #2170 | D59 | semidirect |
| 101. C59 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426346 | 2 |
| #21426172 | 2 |
| #21422172 | 2 |
| #21422132 | 2 |
| C59×#2170 | 2 |
| #12436 | 59 |