Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
206 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C22⋊C4 |
| commutator | C22 | C2×C42 |
| Frattini, cosocle | C24 | C23 |
| socle | C22 | C2×C22⋊C4 |
| prime radical | C22×D4 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×C22⋊C4 | C2 | semidirect |
| 4. #342 | C2 | semidirect |
| 6. C23×C4 | C4 | semidirect |
| 10. C2×C4⋊C4 | C4 | semidirect |
| 11. C2×C22⋊C4 | C4 | semidirect |
| 15. C2×C42 | C4 | semidirect |
| 16. #99 | C4 | direct (N × H) |
| 39. C22⋊C4 | C2×C4 | semidirect |
| 49. C23 | C42 | semidirect |
| 70. C2×C4 | C42 | semidirect |
| 95. C4 | #99 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4 | 2 |
| C2×#99 | 2 |
| C4×C22⋊C4 | 2 |
| #342 | 2 |