Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
346 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26038914 | C2 | semidirect |
| 2. #26038456 | C2 | semidirect |
| 3. #26038444 | C2 | semidirect |
| 4. #26038413 | C2 | semidirect |
| 5. #26038210 | C2 | semidirect |
| 6. #26038196 | C2 | semidirect |
| 22. C2×SD16×C179 | C4 | semidirect |
| 23. C2×D8×C179 | C4 | semidirect |
| 44. C2×Q8×C179 | C2×C4 | semidirect |
| 50. C2×D4×C179 | C2×C4 | semidirect |
| 59. C2×C8×C179 | C2×C4 | semidirect |
| 115. C179 | #1904 | semidirect |
| 128. C2×SD16 | Dic179 | semidirect |
| 129. C2×D8 | Dic179 | semidirect |
| 146. C2×Q8 | C2×Dic179 | semidirect |
| 152. C2×D4 | C2×Dic179 | semidirect |
| 165. C2×C8 | C2×Dic179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038914 | 2 |
| #26038456 | 2 |
| #26038444 | 2 |
| #26038413 | 2 |
| #26038210 | 2 |
| #26038196 | 2 |
| C2×AGL(1,ℤ/8)×C179 | 2 |
| #1904 | 179 |