Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26038787 | C2 | semidirect |
| 3. #26038517 | C2 | semidirect |
| 4. #26038191 | C2 | semidirect |
| 5. #26038188 | C2 | semidirect |
| 6. #26038182 | C2 | semidirect |
| 7. #476×C179 | C2 | semidirect |
| 82. C179 | #1697 | semidirect |
| 85. #476 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038787 | 2 |
| #26038634 | 2 |
| #26038517 | 2 |
| #26038191 | 2 |
| #26038188 | 2 |
| #26038182 | 2 |
| #476×C179 | 2 |
| #1697 | 179 |