Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
480 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C22×C8 | C23×C79 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×C4×C79 ◁ C2×C22⋊C8×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#3191 | C2 | semidirect |
| 2. C79×#2187 | C2 | semidirect |
| 3. C79×#2184 | C2 | semidirect |
| 4. C79×#1999 | C2 | semidirect |
| 5. C79×#1348 | C2 | semidirect |
| 6. C79×#1347 | C2 | semidirect |
| 7. C79×#1314 | C2 | semidirect |
| 31. C2×Q16×C79 | D4 | semidirect |
| 36. C2×D8×C79 | D4 | semidirect |
| 56. #107×C79 | D4 | semidirect |
| 57. #107×C79 | D4 | semidirect |
| 193. #12104 | C79 | direct (N × H) |
| 202. #3191 | C2×C79 | semidirect |
| 203. #2187 | C2×C79 | semidirect |
| 204. #2184 | C2×C79 | semidirect |
| 205. #1999 | C2×C79 | semidirect |
| 206. #1348 | C2×C79 | semidirect |
| 207. #1347 | C2×C79 | semidirect |
| 208. #1314 | C2×C79 | semidirect |
| 209. C79 | #12104 | direct (N × H) |
| 233. C2×Q16 | D4×C79 | semidirect |
| 238. C2×D8 | D4×C79 | semidirect |
| 258. #107 | D4×C79 | semidirect |
| 259. #107 | D4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3191 | 2 |
| C79×#2187 | 2 |
| C79×#2184 | 2 |
| C79×#1999 | 2 |
| C79×#1348 | 2 |
| C79×#1347 | 2 |
| C79×#1314 | 2 |
| #12104 | 79 |