Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #21437234 | C2 | semidirect |
| 2. #21426408 | C2 | semidirect |
| 3. C2×D1888 | C2 | semidirect |
| 4. #21426217 | C2 | semidirect |
| 5. #21422285 | C2 | semidirect |
| 6. #21422237 | C2 | semidirect |
| 7. C59×#1417 | C2 | semidirect |
| 13. C2×D944 | C22 | semidirect |
| 20. #16837236 | C22 | semidirect |
| 23. C2×C32×C59 | C22 | semidirect |
| 24. C59×#368 | C22 | semidirect |
| 121. #1417 | D59 | semidirect |
| 143. C2×C32 | C2×D59 | semidirect |
| 144. #368 | C2×D59 | semidirect |
| 146. C59 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437234 | 2 |
| #21426408 | 2 |
| C2×D1888 | 2 |
| #21426217 | 2 |
| #21422285 | 2 |
| #21422237 | 2 |
| C59×#1417 | 2 |
| #13669 | 59 |