Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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×D944 | C2 | semidirect |
| 2. C2×#16837818 | C2 | semidirect |
| 3. #21433745 | C2 | semidirect |
| 4. #21426200 | C2 | semidirect |
| 5. #21426183 | C2 | semidirect |
| 6. #21425811 | C2 | semidirect |
| 7. C59×#2158 | C2 | semidirect |
| 16. C2×#14273666 | C22 | semidirect |
| 17. C2×C16×D59 | C22 | semidirect |
| 19. #16837639 | C22 | semidirect |
| 21. #16837202 | C22 | semidirect |
| 24. C59×#367 | C22 | semidirect |
| 25. C59×#366 | C22 | semidirect |
| 50. C2×C16×C59 | D4 | semidirect |
| 130. #2158 | D59 | semidirect |
| 152. #367 | C2×D59 | semidirect |
| 153. #366 | C2×D59 | semidirect |
| 155. C59 | #33607 | semidirect |
| 179. C2×C16 | D236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D944 | 2 |
| C2×#16837818 | 2 |
| #21433745 | 2 |
| #21426200 | 2 |
| #21426183 | 2 |
| #21425811 | 2 |
| C59×#2158 | 2 |
| #33607 | 59 |