Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
558 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 151 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. #21434683 | C2 | semidirect |
| 3. #21426376 | C2 | semidirect |
| 4. #21426351 | C2 | semidirect |
| 5. #21426324 | C2 | semidirect |
| 6. #21426191 | C2 | semidirect |
| 7. #21425951 | C2 | semidirect |
| 8. C4×C16×D59 | C2 | semidirect |
| 9. C59×#2240 | C2 | semidirect |
| 113. C59⋊C16 | #41 | semidirect |
| 135. C4×D59 | SD32 | semidirect |
| 166. #2240 | D59 | semidirect |
| 200. C59 | #33736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434683 | 2 |
| #21434673 | 2 |
| #21426376 | 2 |
| #21426351 | 2 |
| #21426324 | 2 |
| #21426191 | 2 |
| #21425951 | 2 |
| C4×C16×D59 | 2 |
| C59×#2240 | 2 |
| #33736 | 59 |