Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21436518 | C2 | semidirect |
| 2. #21426290 | C2 | semidirect |
| 3. #21426240 | C2 | semidirect |
| 4. #21426183 | C2 | semidirect |
| 5. C4×D944 | C2 | semidirect |
| 6. C16×D236 | C2 | semidirect |
| 7. #21425877 | C2 | semidirect |
| 8. C59×#2252 | C2 | semidirect |
| 114. #2252 | D59 | semidirect |
| 145. C59 | #33908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436518 | 2 |
| #21426290 | 2 |
| #21426240 | 2 |
| #21426183 | 2 |
| C4×D944 | 2 |
| C16×D236 | 2 |
| #21425877 | 2 |
| C59×#2252 | 2 |
| #33908 | 59 |