Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
224 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #23761473 | C2 | semidirect |
| 4. #23761364 | C2 | semidirect |
| 6. #23761318 | C2 | semidirect |
| 7. C8×Q16×C79 | C2 | semidirect |
| 57. Q16×C79 | M16 | semidirect |
| 85. C8×C79 | SD32 | semidirect |
| 108. C8×Q16 | D79 | semidirect |
| 113. C79 | #12071 | semidirect |
| 154. Q16 | #11929607 | semidirect |
| 192. C8 | #14579104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579104 | 2 |
| #23762286 | 2 |
| #23761473 | 2 |
| #23761364 | 2 |
| #23761360 | 2 |
| #23761318 | 2 |
| C8×Q16×C79 | 2 |
| #12071 | 79 |