Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. C22⋊(C223⋊C16) | C2 | semidirect |
| 3. #340×C223 | C2 | semidirect |
| 4. C2×D1784 | C4 | semidirect |
| 7. #20297238 | C4 | semidirect |
| 59. C223 | #1347 | semidirect |
| 63. #340 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28383816 | 2 |
| C22⋊(C223⋊C16) | 2 |
| #340×C223 | 2 |
| #1347 | 223 |