Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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×#16838779 | C2 | semidirect |
| 2. C2×#16838778 | C2 | semidirect |
| 3. C4⋊#14515356 | C2 | semidirect |
| 4. #21440699 | C2 | semidirect |
| 5. C22⋊#14515356 | C2 | semidirect |
| 6. #21440697 | C2 | semidirect |
| 24. #14515356 | D4 | semidirect |
| 43. C2×D241 | M16 | semidirect |
| 55. C241 | #435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838779 | 2 |
| C2×#16838778 | 2 |
| C4⋊#14515356 | 2 |
| #21440699 | 2 |
| C22⋊#14515356 | 2 |
| #21440697 | 2 |
| #21440602 | 2 |
| #435 | 241 |