Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. #21436445 | C2 | semidirect |
| 2. #21426371 | C2 | semidirect |
| 3. #21426275 | C2 | semidirect |
| 4. #21426233 | C2 | semidirect |
| 5. #21426179 | C2 | semidirect |
| 6. C16×D236 | C2 | semidirect |
| 7. #366×D59 | C2 | semidirect |
| 8. C4×D16×C59 | C2 | semidirect |
| 77. C16×C59 | #41 | semidirect |
| 91. D236 | D16 | semidirect |
| 120. C4×D16 | D59 | semidirect |
| 147. C59 | #33901 | semidirect |
| 198. C16 | #11745685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436445 | 2 |
| #21426371 | 2 |
| #21426275 | 2 |
| #21426233 | 2 |
| #21426179 | 2 |
| C16×D236 | 2 |
| #366×D59 | 2 |
| C4×D16×C59 | 2 |
| #33901 | 59 |