Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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. #21426458 | C2 | semidirect |
| 3. C4×#14273660 | C2 | semidirect |
| 4. #21423924 | C2 | semidirect |
| 5. #21423921 | C2 | semidirect |
| 6. #21423783 | C2 | semidirect |
| 7. C59×#2275 | C2 | semidirect |
| 10. C4×#11745669 | C4 | semidirect |
| 31. C4×D236 | C2×C4 | semidirect |
| 35. #14273660 | C2×C4 | semidirect |
| 36. #14273648 | C2×C4 | semidirect |
| 37. #14273647 | C2×C4 | semidirect |
| 39. C4×C59⋊C8 | C2×C4 | semidirect |
| 44. C4×D4×C59 | C2×C4 | semidirect |
| 73. #11745669 | C42 | semidirect |
| 125. #2275 | D59 | semidirect |
| 152. C59 | #20508 | semidirect |
| 163. C4×D4 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11745669 | 2 |
| #21426458 | 2 |
| C4×#14273660 | 2 |
| #21423924 | 2 |
| #21423921 | 2 |
| #21423783 | 2 |
| C59×#2275 | 2 |
| #20508 | 59 |