Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
290 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 290 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C79 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ C82×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#2206 | C2 | semidirect |
| 2. C79×#1712 | C2 | semidirect |
| 3. C8×D8×C79 | C2 | semidirect |
| 4. C79×#1370 | C2 | semidirect |
| 5. C79×#1361 | C2 | semidirect |
| 47. D8×C79 | D8 | semidirect |
| 78. C8×C79 | D16 | semidirect |
| 94. #12424 | C79 | direct (N × H) |
| 100. #2206 | C2×C79 | semidirect |
| 101. #1712 | C2×C79 | semidirect |
| 102. C8×D8 | C2×C79 | semidirect |
| 103. #1370 | C2×C79 | semidirect |
| 104. #1361 | C2×C79 | semidirect |
| 105. C79 | #12424 | direct (N × H) |
| 147. D8 | D8×C79 | semidirect |
| 178. C8 | D16×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#2206 | 2 |
| C79×#1712 | 2 |
| C8×D8×C79 | 2 |
| C79×#1370 | 2 |
| C79×#1361 | 2 |
| #12424 | 79 |