Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
632 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21434104 | C2 | semidirect |
| 2. #21433895 | C2 | semidirect |
| 4. #21422661 | C2 | semidirect |
| 5. #21422486 | C2 | semidirect |
| 6. #21421956 | C2 | semidirect |
| 7. C59×#1486 | C2 | semidirect |
| 37. #14273727 | D4 | semidirect |
| 38. #14273727 | D4 | semidirect |
| 65. C4×C59⋊C8 | D4 | semidirect |
| 81. C4⋊C8×C59 | D4 | semidirect |
| 109. C2×D236 | SD16 | semidirect |
| 235. #1486 | D59 | semidirect |
| 270. C59 | #10000 | semidirect |
| 310. C4⋊C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434104 | 2 |
| #21433895 | 2 |
| #21428997 | 2 |
| #21422661 | 2 |
| #21422486 | 2 |
| #21421956 | 2 |
| C59×#1486 | 2 |
| #10000 | 59 |