Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
312 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 86 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×C79 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C79 |
| prime radical | C79×#2206 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ C8×Q8×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#3380 | C2 | semidirect |
| 2. C79×#2240 | C2 | semidirect |
| 4. C79×#1668 | C2 | semidirect |
| 5. C79×#1365 | C2 | semidirect |
| 6. C79×Q8⋊C16 | C2 | semidirect |
| 7. C79×#1331 | C2 | semidirect |
| 66. D8×C79 | SD16 | semidirect |
| 127. #12355 | C79 | direct (N × H) |
| 133. #3380 | C2×C79 | semidirect |
| 134. #2240 | C2×C79 | semidirect |
| 136. #1668 | C2×C79 | semidirect |
| 137. #1365 | C2×C79 | semidirect |
| 138. Q8⋊C16 | C2×C79 | semidirect |
| 139. #1331 | C2×C79 | semidirect |
| 140. C79 | #12355 | direct (N × H) |
| 199. D8 | SD16×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3380 | 2 |
| C79×#2240 | 2 |
| C79×#2206 | 2 |
| C79×#1668 | 2 |
| C79×#1365 | 2 |
| C79×Q8⋊C16 | 2 |
| C79×#1331 | 2 |
| #12355 | 79 |