Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
173 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4 |
| Frattini, cosocle | C22×C4 | C23 |
| prime radical | C2×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #407 | C2 | semidirect |
| 3. C4×C22⋊C4 | C2 | semidirect |
| 4. #327 | C2 | semidirect |
| 6. C22×D4 | C4 | semidirect |
| 11. #121 | C4 | semidirect |
| 13. C2×C4⋊C4 | C4 | semidirect |
| 18. C22⋊C8 | C22 | semidirect |
| 19. #95 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121 | 2 |
| #407 | 2 |
| C4×C22⋊C4 | 2 |
| #327 | 2 |