Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21437232 | C2 | semidirect |
| 2. #21437230 | C2 | semidirect |
| 3. #21434539 | C2 | semidirect |
| 4. #21425823 | C2 | semidirect |
| 5. #21424987 | C2 | semidirect |
| 6. #21422175 | C2 | semidirect |
| 7. C59×#2143 | C2 | semidirect |
| 48. C2×Dic236 | D4 | semidirect |
| 55. C2×D472 | D4 | semidirect |
| 75. C2×C59⋊C16 | D4 | semidirect |
| 92. C2×C16×C59 | D4 | semidirect |
| 232. #2143 | D59 | semidirect |
| 269. C59 | #13340 | semidirect |
| 323. C2×C16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437232 | 2 |
| #21437230 | 2 |
| #21434539 | 2 |
| #21425823 | 2 |
| #21424987 | 2 |
| #21422175 | 2 |
| C59×#2143 | 2 |
| #13340 | 59 |