Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
930 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 235 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. C22×#14273672 | C2 | semidirect |
| 2. C22×D944 | C2 | semidirect |
| 3. C2×#16837786 | C2 | semidirect |
| 4. C2×#16837779 | C2 | semidirect |
| 5. #21426362 | C2 | direct (N × H) |
| 6. C2×C59×#346 | C2 | semidirect |
| 15. C2×#14273672 | C22 | semidirect |
| 17. C2×D944 | C22 | semidirect |
| 19. #16837786 | C22 | semidirect |
| 21. #16837779 | C22 | semidirect |
| 24. C59×#346 | C22 | semidirect |
| 53. C2×C16×C59 | D4 | semidirect |
| 93. C16×C59 | C2×D4 | semidirect |
| 142. C2×#346 | D59 | semidirect |
| 143. C2×C59 | #2250 | semidirect |
| 165. #346 | C2×D59 | semidirect |
| 166. C59 | C2×#2250 | semidirect |
| 195. C2×C16 | D236 | semidirect |
| 235. C16 | C2×D236 | semidirect |
| 280. C2 | #21426362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273672 | 2 |
| C22×D944 | 2 |
| C2×#16837786 | 2 |
| C2×#16837779 | 2 |
| #21426362 | 2 |
| C2×C59×#346 | 2 |
| C2×#2250 | 59 |