Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D101 |
| commutator, socle, cosocle | C23×C101 | C24 |
| Fitting | #380×C101 | C2 |
| prime radical | C24×D101 | C22 |
| hypercenter | #380 | D101 |
| hypocenter | C101 | #2848 |
| LCS | G ▷ C23×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#15692235 | C2 | semidirect |
| 3. C2×#15692234 | C2 | semidirect |
| 4. #20265052 | C2 | semidirect |
| 5. #20265051 | C2 | semidirect |
| 6. #20265034 | C2 | semidirect |
| 8. #380×C101 | C2 | semidirect |
| 10. C22×Dic202 | C22 | semidirect |
| 18. C2×C4⋊Dic101 | C22 | semidirect |
| 19. C2×C4⋊Dic101 | C22 | semidirect |
| 20. C2×#13108053 | C22 | semidirect |
| 24. #15692162 | C22 | semidirect |
| 26. C2×C4⋊C4×C101 | C22 | semidirect |
| 28. #95×C101 | C22 | semidirect |
| 33. C23×D101 | Q8 | semidirect |
| 104. C22×C101 | C22⋊Q8 | semidirect |
| 117. C2×D101 | C22⋊Q8 | semidirect |
| 132. C101 | #2848 | semidirect |
| 139. #380 | D101 | semidirect |
| 154. C2×C4⋊C4 | C2×D101 | semidirect |
| 160. #95 | C2×D101 | semidirect |
| 244. C22 | #15692235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D101 | 2 |
| C2×#15692235 | 2 |
| C2×#15692234 | 2 |
| #20265052 | 2 |
| #20265051 | 2 |
| #20265034 | 2 |
| #20265032 | 2 |
| #380×C101 | 2 |
| #2848 | 101 |