Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26012558 | C2 | semidirect |
| 2. #26012490 | C2 | semidirect |
| 3. #26012483 | C2 | semidirect |
| 4. #26012472 | C2 | semidirect |
| 5. #26012373 | C2 | semidirect |
| 6. #26012359 | C2 | semidirect |
| 22. C2×#14583813 | C4 | semidirect |
| 23. C2×D1384 | C4 | semidirect |
| 24. C2×#14583811 | C4 | semidirect |
| 26. C2×SD16×C173 | C4 | semidirect |
| 48. C2×D692 | C2×C4 | semidirect |
| 61. C2×#13063436 | C2×C4 | semidirect |
| 62. C2×Q8×C173 | C2×C4 | semidirect |
| 65. C2×C8×C173 | C2×C4 | semidirect |
| 128. C173 | #1904 | semidirect |
| 142. C2×SD16 | #10621924 | semidirect |
| 161. C2×Q8 | C2×#10621924 | semidirect |
| 184. C2×C8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012558 | 2 |
| #26012490 | 2 |
| #26012483 | 2 |
| #26012472 | 2 |
| #26012373 | 2 |
| #26012359 | 2 |
| C2×#19149706 | 2 |
| #1904 | 173 |