Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2078 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 627 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. C22×Dic472 | C2 | semidirect |
| 3. C22×#14273673 | C2 | semidirect |
| 4. C2×Q32×D59 | C2 | direct (N × H) |
| 6. C22×Q32×C59 | C2 | semidirect |
| 13. C2×Dic472 | C22 | semidirect |
| 14. C2×#14273673 | C22 | semidirect |
| 15. Q32×D59 | C22 | direct (N × H) |
| 19. C2×Q32×C59 | C22 | semidirect |
| 35. Dic472 | C23 | semidirect |
| 36. #14273673 | C23 | semidirect |
| 43. Q32×C59 | C23 | semidirect |
| 73. C22×D59 | Q32 | direct (N × H) |
| 92. C22×C59 | C2×Q32 | semidirect |
| 94. C2×D59 | C2×Q32 | direct (N × H) |
| 105. C22×Q32 | D59 | direct (N × H) |
| 107. C2×C59 | C22×Q32 | semidirect |
| 109. D59 | C22×Q32 | direct (N × H) |
| 120. C2×Q32 | C2×D59 | direct (N × H) |
| 124. C59 | C23×Q32 | semidirect |
| 145. Q32 | C22×D59 | direct (N × H) |
| 197. C22 | Q32×D59 | direct (N × H) |
| 205. C2 | C2×Q32×D59 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×D59 | 2 |
| C22×Dic472 | 2 |
| C22×#14273673 | 2 |
| C2×Q32×D59 | 2 |
| C22×C16×D59 | 2 |
| C22×Q32×C59 | 2 |
| C23×Q32 | 59 |