Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26039239 | C2 | semidirect |
| 2. C2×#19153141 | C2 | semidirect |
| 3. #26039008 | C2 | semidirect |
| 4. #26038455 | C2 | semidirect |
| 5. #26038445 | C2 | semidirect |
| 6. #26038412 | C2 | semidirect |
| 7. #344×C179 | C2 | semidirect |
| 41. C2×Dic358 | D4 | semidirect |
| 50. C2×D716 | D4 | semidirect |
| 69. M16×C179 | D4 | semidirect |
| 71. C2×C8×C179 | D4 | semidirect |
| 142. C179 | #2008 | semidirect |
| 150. #344 | D179 | semidirect |
| 208. M16 | D716 | semidirect |
| 210. C2×C8 | D716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039239 | 2 |
| C2×#19153141 | 2 |
| #26039008 | 2 |
| #26038455 | 2 |
| #26038445 | 2 |
| #26038412 | 2 |
| #344×C179 | 2 |
| #2008 | 179 |