Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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 | C22×D4×C101 | C22 |
| hypercenter | #390 | D101 |
| hypocenter | C101 | #2861 |
| 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×#15692246 | C2 | semidirect |
| 3. #20265083 | C2 | semidirect |
| 4. #20265082 | C2 | semidirect |
| 6. #20265070 | C2 | semidirect |
| 7. #20265065 | C2 | semidirect |
| 8. C42×Dic101 | C2 | semidirect |
| 110. C101 | #2861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692246 | 2 |
| C2×#15692242 | 2 |
| #20265083 | 2 |
| #20265082 | 2 |
| #20265080 | 2 |
| #20265070 | 2 |
| #20265065 | 2 |
| C42×Dic101 | 2 |
| #390×C101 | 2 |
| #2861 | 101 |