Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
140 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | #99 |
| commutator | C22×C4 | C2×C4×C101 |
| Frattini, cosocle | C2×C4⋊C4 | C22×C101 |
| prime radical | C23×C101 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C101 ◁ C2×C4⋊C4×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 59. #1354 | C101 | direct (N × H) |
| 60. C101 | #1354 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #395×C101 | 2 |
| #343×C101 | 2 |
| #324×C101 | 2 |
| #1354 | 101 |