Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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. #23776375 | C2 | semidirect |
| 2. #23765625 | C2 | semidirect |
| 3. #23765534 | C2 | semidirect |
| 4. #23765435 | C2 | semidirect |
| 5. Q8×C79⋊C16 | C2 | semidirect |
| 6. C4×#14579102 | C2 | semidirect |
| 7. Q8×D8×C79 | C2 | semidirect |
| 64. D8×C79 | #41 | semidirect |
| 75. Q8×C79 | D16 | semidirect |
| 112. Q8×D8 | D79 | semidirect |
| 118. C79 | #33925 | semidirect |
| 171. D8 | #11929625 | semidirect |
| 186. Q8 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776375 | 2 |
| #23765625 | 2 |
| #23765534 | 2 |
| #23765435 | 2 |
| Q8×C79⋊C16 | 2 |
| C4×#14579102 | 2 |
| Q8×D8×C79 | 2 |
| #33925 | 79 |