Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21426240 | C2 | semidirect |
| 3. #21423492 | C2 | semidirect |
| 4. #21422142 | C2 | semidirect |
| 5. #21422058 | C2 | semidirect |
| 6. #21422052 | C2 | semidirect |
| 7. C59×#2240 | C2 | semidirect |
| 17. C4⋊(C59⋊C16) | C22 | semidirect |
| 19. #16837155 | C22 | semidirect |
| 21. C59×#500 | C22 | semidirect |
| 24. C4×C16×C59 | C22 | semidirect |
| 145. #2240 | D59 | semidirect |
| 159. #500 | C2×D59 | semidirect |
| 171. C4×C16 | 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 |
|---|---|
| #21435771 | 2 |
| #21426240 | 2 |
| #21423492 | 2 |
| #21422142 | 2 |
| #21422058 | 2 |
| #21422052 | 2 |
| C59×#2240 | 2 |
| #12372 | 59 |