Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19153141 | C2 | semidirect |
| 2. C2×#19153138 | C2 | semidirect |
| 3. #26039017 | C2 | semidirect |
| 4. C2×#19153041 | C2 | semidirect |
| 5. #26038341 | C2 | semidirect |
| 6. #26038207 | C2 | semidirect |
| 7. C2×#104×C179 | C2 | semidirect |
| 43. C2×D716 | D4 | semidirect |
| 53. #15668243 | D4 | semidirect |
| 72. M16×C179 | D4 | semidirect |
| 152. C179 | #2006 | semidirect |
| 158. C2×#104 | D179 | semidirect |
| 218. M16 | C22⋊D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153141 | 2 |
| C2×#19153138 | 2 |
| #26039017 | 2 |
| C2×#19153041 | 2 |
| #26038341 | 2 |
| #26038207 | 2 |
| C2×#104×C179 | 2 |
| #2006 | 179 |