Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
914 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D163 |
| commutator, socle, cosocle | C23×C163 | C24 |
| Fitting | C2×#95×C163 | C2 |
| hypercenter | C2×#95 | D163 |
| hypocenter | C163 | #2430 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14579699 | C2 | semidirect |
| 2. C2×#19104718 | C2 | semidirect |
| 3. C2×#19104709 | C2 | semidirect |
| 4. #23781586 | C2 | semidirect |
| 5. #23781583 | C2 | semidirect |
| 6. #23781578 | C2 | semidirect |
| 7. #23781575 | C2 | semidirect |
| 8. #23781544 | C2 | semidirect |
| 9. #23781543 | C2 | semidirect |
| 10. #23781539 | C2 | semidirect |
| 11. C2×#95×C163 | C2 | semidirect |
| 53. C2×C22⋊D163 | D4 | semidirect |
| 76. C22×C4×C163 | D4 | semidirect |
| 126. C2×C4×C163 | #41 | semidirect |
| 165. C163 | #2430 | semidirect |
| 177. C2×#95 | D163 | semidirect |
| 232. C22×C4 | D652 | semidirect |
| 292. C2×C4 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104718 | 2 |
| C2×#19104709 | 2 |
| #23781586 | 2 |
| #23781583 | 2 |
| #23781578 | 2 |
| #23781575 | 2 |
| #23781544 | 2 |
| #23781543 | 2 |
| #23781539 | 2 |
| C2×#95×C163 | 2 |
| #2430 | 163 |