Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#16837225 | C2 | semidirect |
| 3. C2×#16837224 | C2 | semidirect |
| 6. #21422196 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 19. (C2×D59)⋊C16 | C4 | semidirect |
| 40. C2×C59⋊C16 | C2×C4 | semidirect |
| 52. C2×C16×C59 | C2×C4 | semidirect |
| 135. C2×D59 | #365 | semidirect |
| 149. #1383 | D59 | semidirect |
| 171. C59 | #12929 | semidirect |
| 194. C2×C16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#106×D59 | 2 |
| C2×#16837225 | 2 |
| C2×#16837224 | 2 |
| #21425706 | 2 |
| #21424131 | 2 |
| #21422196 | 2 |
| C59×#1383 | 2 |
| #12929 | 59 |