Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
210 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C79 | C2×D8 |
| commutator | C2×C8 | C22×C4×C79 |
| Frattini, cosocle | C4×C8 | C23×C79 |
| socle, prime radical | C22×C79 | C4×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C79 ◁ C4×C8×C79 ◁ C82×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 83. C8×C79 | Q32 | semidirect |
| 96. #12072 | C79 | direct (N × H) |
| 107. C79 | #12072 | direct (N × H) |
| 183. C8 | Q32×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q32×C79 | 2 |
| C79×#1591 | 2 |
| C8×Q16×C79 | 2 |
| C79×#1371 | 2 |
| C79×#1332 | 2 |
| C79×#1312 | 2 |
| #12072 | 79 |