Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837840 | C2 | semidirect |
| 2. C2×#16837837 | C2 | semidirect |
| 3. #21434539 | C2 | semidirect |
| 4. C2×#16837211 | C2 | semidirect |
| 5. #21424970 | C2 | semidirect |
| 6. #21422179 | C2 | semidirect |
| 7. C2×C59×#360 | C2 | semidirect |
| 52. C2×D472 | D4 | semidirect |
| 68. #14273667 | D4 | semidirect |
| 84. M32×C59 | D4 | semidirect |
| 226. C2×#360 | D59 | semidirect |
| 261. C59 | #13341 | semidirect |
| 309. M32 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837840 | 2 |
| C2×#16837837 | 2 |
| #21434539 | 2 |
| C2×#16837211 | 2 |
| #21424970 | 2 |
| #21422179 | 2 |
| C2×C59×#360 | 2 |
| #13341 | 59 |