Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1322 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1322 conjugacy classes of subgroups — too many to draw. Only its 259 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. C2×C4×D472 | C2 | semidirect |
| 2. C4×#14273724 | C2 | semidirect |
| 3. #21425623 | C2 | semidirect |
| 4. #21425169 | C2 | semidirect |
| 5. C59×#1744 | C2 | semidirect |
| 38. C4×C8×C59 | D4 | semidirect |
| 58. C42×C59 | D8 | semidirect |
| 106. #1744 | D59 | semidirect |
| 125. C59 | #23798 | semidirect |
| 145. C4×C8 | D236 | semidirect |
| 170. C42 | D472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D472 | 2 |
| C4×#14273724 | 2 |
| #21425623 | 2 |
| #21425169 | 2 |
| C59×#1744 | 2 |
| #23798 | 59 |