Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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×#10620284 | C2 | semidirect |
| 2. C2×#10620282 | C2 | semidirect |
| 3. #13050138 | C2 | semidirect |
| 4. #13050088 | C2 | semidirect |
| 5. #13050085 | C2 | semidirect |
| 6. C22⋊#66491 | C2 | semidirect |
| 7. C2×#41×C41 | C2 | semidirect |
| 27. Q8×C41 | D4 | semidirect |
| 30. D4×C41 | D4 | semidirect |
| 65. C41 | #449 | semidirect |
| 66. C2×#41 | D41 | semidirect |
| 92. Q8 | C22⋊D41 | semidirect |
| 98. D4 | C22⋊D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620284 | 2 |
| C2×#10620282 | 2 |
| #13050138 | 2 |
| #13050088 | 2 |
| #13050085 | 2 |
| C22⋊#66491 | 2 |
| C2×#41×C41 | 2 |
| #449 | 41 |