Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23782482 | C2 | semidirect |
| 2. #23782106 | C2 | semidirect |
| 3. #23782105 | C2 | semidirect |
| 4. #23782095 | C2 | semidirect |
| 5. C2×#19104681 | C2 | semidirect |
| 6. #23782082 | C2 | semidirect |
| 7. #578×C163 | C2 | semidirect |
| 73. C163 | #3417 | semidirect |
| 76. #578 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782482 | 2 |
| #23782106 | 2 |
| #23782105 | 2 |
| #23782095 | 2 |
| C2×#19104681 | 2 |
| #23782082 | 2 |
| #578×C163 | 2 |
| #3417 | 163 |