Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#19153054 | C2 | semidirect |
| 2. C2×C16×D179 | C2 | semidirect |
| 3. #26038676 | C2 | semidirect |
| 4. #26038672 | C2 | semidirect |
| 5. #26038264 | C2 | semidirect |
| 6. #26038241 | C2 | semidirect |
| 7. #357×C179 | C2 | semidirect |
| 33. C179⋊C16 | D4 | semidirect |
| 67. C2×D179 | D16 | semidirect |
| 79. C179 | #2215 | semidirect |
| 87. #357 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153054 | 2 |
| C2×C16×D179 | 2 |
| #26038676 | 2 |
| #26038672 | 2 |
| #26038264 | 2 |
| #26038241 | 2 |
| #357×C179 | 2 |
| #2215 | 179 |