Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21425973 | C2 | semidirect |
| 3. #21422303 | C2 | semidirect |
| 4. #21422285 | C2 | semidirect |
| 5. #21422283 | C2 | semidirect |
| 6. #21422232 | C2 | semidirect |
| 7. C59×#2179 | C2 | semidirect |
| 10. #16837239 | C4 | semidirect |
| 11. #16837237 | C4 | semidirect |
| 28. C59⋊C32 | C2×C4 | semidirect |
| 31. Q32×C59 | C2×C4 | semidirect |
| 33. D16×C59 | C2×C4 | semidirect |
| 85. #2179 | D59 | semidirect |
| 108. C59 | #13658 | semidirect |
| 113. Q32 | C4×D59 | semidirect |
| 117. D16 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426408 | 2 |
| #21425973 | 2 |
| #21422303 | 2 |
| #21422285 | 2 |
| #21422283 | 2 |
| #21422232 | 2 |
| C59×#2179 | 2 |
| #13658 | 59 |