Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
484 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C4×#14273749 | C2 | semidirect |
| 3. #21425832 | C2 | semidirect |
| 4. #21425823 | C2 | semidirect |
| 5. #21422210 | C2 | semidirect |
| 6. #21422178 | C2 | semidirect |
| 7. C59×#1974 | C2 | semidirect |
| 10. #16837843 | C4 | semidirect |
| 12. #16837838 | C4 | semidirect |
| 50. #14273667 | C2×C4 | semidirect |
| 62. C2×Q16×C59 | C2×C4 | semidirect |
| 64. C2×D8×C59 | C2×C4 | semidirect |
| 190. #1974 | D59 | semidirect |
| 220. C59 | #13027 | semidirect |
| 232. C2×Q16 | C4×D59 | semidirect |
| 236. C2×D8 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437230 | 2 |
| C4×#14273749 | 2 |
| #21425832 | 2 |
| #21425823 | 2 |
| #21422210 | 2 |
| #21422178 | 2 |
| C59×#1974 | 2 |
| #13027 | 59 |