Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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. C16×D236 | C2 | semidirect |
| 2. #21423482 | C2 | semidirect |
| 4. #21422168 | C2 | semidirect |
| 5. #21422151 | C2 | semidirect |
| 6. #21422142 | C2 | semidirect |
| 7. C59×#2240 | C2 | semidirect |
| 109. #2240 | 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 |
|---|---|
| C16×D236 | 2 |
| #21423482 | 2 |
| #21423448 | 2 |
| #21422168 | 2 |
| #21422151 | 2 |
| #21422142 | 2 |
| C59×#2240 | 2 |
| #12467 | 59 |