Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ #436×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C79×#3277 | C2 | semidirect |
| 2. C79×#2250 | C2 | semidirect |
| 3. C79×#2207 | C2 | semidirect |
| 4. C79×#1687 | C2 | semidirect |
| 5. C79×#1360 | C2 | semidirect |
| 6. C79×#1334 | C2 | semidirect |
| 7. C79×#1330 | C2 | semidirect |
| 85. Q16×C79 | D8 | semidirect |
| 166. #12325 | C79 | direct (N × H) |
| 173. #3277 | C2×C79 | semidirect |
| 174. #2250 | C2×C79 | semidirect |
| 175. #2207 | C2×C79 | semidirect |
| 176. #1687 | C2×C79 | semidirect |
| 177. #1360 | C2×C79 | semidirect |
| 178. #1334 | C2×C79 | semidirect |
| 179. #1330 | C2×C79 | semidirect |
| 180. C79 | #12325 | direct (N × H) |
| 258. Q16 | D8×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#3277 | 2 |
| C79×#2250 | 2 |
| C79×#2207 | 2 |
| C79×#1687 | 2 |
| C79×#1360 | 2 |
| C79×#1334 | 2 |
| C79×#1330 | 2 |
| #12325 | 79 |