Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
162 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D4 |
| commutator | C2×C4 | C22×C4 |
| Frattini, cosocle | C22×C4 | C23 |
| socle | C22 | C4×D4 |
| prime radical | C2×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#131 | C2 | semidirect |
| 3. C2×#104 | C2 | semidirect |
| 4. C2×#104 | C2 | semidirect |
| 5. #408 | C2 | semidirect |
| 6. #341 | C2 | semidirect |
| 7. #336 | C2 | semidirect |
| 12. C2×Q16 | C4 | semidirect |
| 13. C2×SD16 | C4 | semidirect |
| 14. C2×SD16 | C4 | semidirect |
| 15. C2×D8 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135 | 2 |
| C2×#131 | 2 |
| C2×#104 | 2 |
| #408 | 2 |
| #341 | 2 |
| #336 | 2 |