Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21426136 | C2 | semidirect |
| 3. Q16×C59⋊C8 | C2 | semidirect |
| 4. #21422165 | C2 | semidirect |
| 5. #21422143 | C2 | semidirect |
| 6. #21422142 | C2 | semidirect |
| 7. C59×#2207 | C2 | semidirect |
| 54. Q16×C59 | D8 | semidirect |
| 101. C59⋊C8 | SD32 | semidirect |
| 118. #2207 | D59 | semidirect |
| 144. C59 | #12425 | semidirect |
| 176. Q16 | #11745669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426136 | 2 |
| #21423710 | 2 |
| Q16×C59⋊C8 | 2 |
| #21422165 | 2 |
| #21422143 | 2 |
| #21422142 | 2 |
| C59×#2207 | 2 |
| #12425 | 59 |