Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#16837844 | C2 | semidirect |
| 3. #494×D59 | C2 | semidirect |
| 4. #21426364 | C2 | semidirect |
| 5. #21426353 | C2 | semidirect |
| 6. #21426352 | C2 | semidirect |
| 7. #21426348 | C2 | semidirect |
| 8. C4×#14273666 | C2 | semidirect |
| 9. C59×#2247 | C2 | semidirect |
| 64. #14273666 | D4 | semidirect |
| 158. C4×C59 | #510 | semidirect |
| 171. #2247 | D59 | semidirect |
| 203. C59 | #33718 | semidirect |
| 328. C4 | #16837844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837844 | 2 |
| #21434525 | 2 |
| #494×D59 | 2 |
| #21426364 | 2 |
| #21426353 | 2 |
| #21426352 | 2 |
| #21426348 | 2 |
| C4×#14273666 | 2 |
| C59×#2247 | 2 |
| #33718 | 59 |