Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 230 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. #21422915 | C2 | semidirect |
| 3. #21422162 | C2 | semidirect |
| 4. #21422066 | C2 | semidirect |
| 6. #21422016 | C2 | semidirect |
| 36. SD32×C59 | C8 | semidirect |
| 48. Q16×C59 | C2×C8 | semidirect |
| 65. C16×C59 | C2×C8 | semidirect |
| 125. C59 | #12065 | semidirect |
| 131. SD32 | C59⋊C8 | semidirect |
| 151. Q16 | C2×C59⋊C8 | semidirect |
| 169. C16 | C2×C59⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422920 | 2 |
| #21422915 | 2 |
| #21422162 | 2 |
| #21422066 | 2 |
| #21422063 | 2 |
| #21422016 | 2 |
| C59×#2175 | 2 |
| #12065 | 59 |