Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
260 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 104 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, Frattini, cosocle | C2×C4 | C24 |
| socle | C22 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#135 | C2 | semidirect |
| 2. C23×C8 | C2 | semidirect |
| 3. #525 | C2 | semidirect |
| 4. #467 | C2 | semidirect |
| 5. #466 | C2 | semidirect |
| 6. #465 | C2 | semidirect |
| 7. #427 | C2 | semidirect |
| 8. #416 | C2 | semidirect |
| 12. C2×Q16 | C22 | semidirect |
| 13. C2×SD16 | C22 | semidirect |
| 14. C2×D8 | C22 | semidirect |
| 26. #107 | C22 | semidirect |
| 27. #106 | C22 | semidirect |
| 28. #103 | C22 | semidirect |
| 29. #102 | C22 | semidirect |
| 50. C2×C8 | D4 | semidirect |
| 93. C22 | #135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135 | 2 |
| C23×C8 | 2 |
| #525 | 2 |
| #467 | 2 |
| #466 | 2 |
| #465 | 2 |
| #427 | 2 |
| #416 | 2 |