Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
344 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C101 | C2×D4 |
| commutator | C2×C4 | C22×C4×C101 |
| Frattini, cosocle | C22×C4 | C23×C101 |
| prime radical | C22×D4×C101 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4⋊C8×C101 | C2 | semidirect |
| 3. C2×#103×C101 | C2 | semidirect |
| 5. C4×C4⋊C4×C101 | C2 | semidirect |
| 10. #124×C101 | C4 | semidirect |
| 94. #1983 | C101 | direct (N × H) |
| 95. C101 | #1983 | direct (N × H) |
| 97. C2×C4⋊C8 | C2×C101 | semidirect |
| 98. C2×#103 | C2×C101 | semidirect |
| 100. C4×C4⋊C4 | C2×C101 | semidirect |
| 105. #124 | C4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C101 | 2 |
| C2×C4⋊C8×C101 | 2 |
| C2×#103×C101 | 2 |
| C2×#102×C101 | 2 |
| C4×C4⋊C4×C101 | 2 |
| #1983 | 101 |