Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#20296319 | C2 | semidirect |
| 4. #28380668 | C2 | semidirect |
| 5. #28380667 | C2 | semidirect |
| 7. C2×Q16×C439 | C2 | semidirect |
| 45. C2×D439 | Q16 | semidirect |
| 57. C439 | #451 | semidirect |
| 61. C2×Q16 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D439 | 2 |
| C2×#20296319 | 2 |
| #28380719 | 2 |
| #28380668 | 2 |
| #28380667 | 2 |
| (C2×D439)⋊C8 | 2 |
| C2×Q16×C439 | 2 |
| #451 | 439 |