Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
752 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 177 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 | #390×C101 | C2 |
| prime radical | C2×#15692251 | C2 |
| hypercenter | #390 | D101 |
| hypocenter | C101 | #2858 |
| LCS | G ▷ C23×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15692254 | C2 | semidirect |
| 3. C2×#15692241 | C2 | semidirect |
| 4. #20265080 | C2 | semidirect |
| 5. #20265079 | C2 | semidirect |
| 6. #20265078 | C2 | semidirect |
| 7. #20265077 | C2 | semidirect |
| 8. C42×Dic101 | C2 | semidirect |
| 9. #390×C101 | C2 | semidirect |
| 52. C4×Dic101 | D4 | semidirect |
| 113. C4×C101 | #124 | semidirect |
| 116. Dic101 | #124 | semidirect |
| 126. C101 | #2858 | semidirect |
| 134. #390 | D101 | semidirect |
| 243. C4 | #15692241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692254 | 2 |
| C2×#15692251 | 2 |
| C2×#15692241 | 2 |
| #20265080 | 2 |
| #20265079 | 2 |
| #20265078 | 2 |
| #20265077 | 2 |
| C42×Dic101 | 2 |
| #390×C101 | 2 |
| #2858 | 101 |