Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 240 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. #21426321 | C2 | semidirect |
| 2. D4×C59⋊C16 | C2 | semidirect |
| 4. #21422167 | C2 | semidirect |
| 5. #21422151 | C2 | semidirect |
| 6. #21422141 | C2 | semidirect |
| 7. C59×#1673 | C2 | semidirect |
| 111. #1673 | D59 | semidirect |
| 136. C59 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426321 | 2 |
| D4×C59⋊C16 | 2 |
| #21423451 | 2 |
| #21422167 | 2 |
| #21422151 | 2 |
| #21422141 | 2 |
| C59×#1673 | 2 |
| #12467 | 59 |