Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
408 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 149 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, prime radical, cosocle | C23×C101 | C24 |
| Fitting | #383×C101 | C2 |
| hypercenter | #383 | D101 |
| hypocenter | C101 | #2863 |
| LCS | G ▷ C23×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 34. C42×C101 | Q8 | semidirect |
| 66. C101 | #2863 | semidirect |
| 100. C42 | Dic202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265081 | 2 |
| #20265074 | 2 |
| #20265064 | 2 |
| #20265060 | 2 |
| #20265045 | 2 |
| C42×Dic101 | 2 |
| #383×C101 | 2 |
| #2863 | 101 |