Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1150 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 211 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×#16837515 | C2 | semidirect |
| 2. C2×C4×D472 | C2 | semidirect |
| 3. #21426821 | C2 | semidirect |
| 4. #21425616 | C2 | semidirect |
| 5. #21425169 | C2 | semidirect |
| 6. C59×#1746 | C2 | semidirect |
| 46. #97×C59 | D4 | semidirect |
| 47. C4×C8×C59 | D4 | semidirect |
| 119. #1746 | D59 | semidirect |
| 141. C59 | #23810 | semidirect |
| 163. #97 | D236 | semidirect |
| 164. C4×C8 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837515 | 2 |
| C2×C4×D472 | 2 |
| #21426821 | 2 |
| #21425616 | 2 |
| #21425169 | 2 |
| C59×#1746 | 2 |
| #23810 | 59 |