Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21426320 | C2 | semidirect |
| 3. #21426243 | C2 | semidirect |
| 4. #21423496 | C2 | semidirect |
| 5. #21422141 | C2 | semidirect |
| 6. #21422052 | C2 | semidirect |
| 7. C59×#1331 | C2 | semidirect |
| 10. #16837807 | C22 | semidirect |
| 18. C4⋊(C59⋊C16) | C22 | semidirect |
| 23. C4×C16×C59 | C22 | semidirect |
| 24. C59×#335 | C22 | semidirect |
| 149. #1331 | D59 | semidirect |
| 171. C4×C16 | C2×D59 | semidirect |
| 172. #335 | C2×D59 | semidirect |
| 174. C59 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D236 | 2 |
| #21426320 | 2 |
| #21426243 | 2 |
| #21423496 | 2 |
| #21422141 | 2 |
| #21422052 | 2 |
| C59×#1331 | 2 |
| #12372 | 59 |