Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2334 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 747 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×#14273670 | C2 | direct (N × H) |
| 3. C23×C59⋊C16 | C2 | semidirect |
| 4. C23×Q16×C59 | C2 | semidirect |
| 8. C2×#14273670 | C22 | direct (N × H) |
| 9. C22×C59⋊C16 | C22 | semidirect |
| 12. C22×Q16×C59 | C22 | semidirect |
| 19. #14273670 | C23 | direct (N × H) |
| 20. C2×C59⋊C16 | C23 | semidirect |
| 26. C2×Q16×C59 | C23 | semidirect |
| 40. Q16×C59 | C24 | semidirect |
| 45. C59⋊C16 | C24 | semidirect |
| 46. C23×C59 | SD32 | semidirect |
| 60. C22×C59 | C2×SD32 | semidirect |
| 67. C23×Q16 | D59 | semidirect |
| 71. C2×C59 | C22×SD32 | semidirect |
| 77. C22×Q16 | C2×D59 | semidirect |
| 83. C59 | C23×SD32 | semidirect |
| 92. C2×Q16 | C22×D59 | semidirect |
| 110. Q16 | C23×D59 | semidirect |
| 118. C23 | #14273670 | direct (N × H) |
| 131. C22 | C2×#14273670 | direct (N × H) |
| 137. C2 | C22×#14273670 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D472 | 2 |
| C22×#14273670 | 2 |
| C23×C59⋊C16 | 2 |
| C23×Q16×C59 | 2 |
| C23×SD32 | 59 |