Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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. C8×Dic236 | C2 | semidirect |
| 3. #21422169 | C2 | semidirect |
| 4. #21422059 | C2 | semidirect |
| 6. #21422014 | C2 | semidirect |
| 64. Dic236 | M16 | semidirect |
| 85. C8×C59 | SD32 | semidirect |
| 128. C59 | #12071 | semidirect |
| 192. C8 | #14273671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273671 | 2 |
| C8×Dic236 | 2 |
| #21422169 | 2 |
| #21422059 | 2 |
| #21422057 | 2 |
| #21422014 | 2 |
| C59×#1589 | 2 |
| #12071 | 59 |