Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. M32×D179 | C2 | semidirect |
| 3. #26038221 | C2 | semidirect |
| 4. #26038220 | C2 | semidirect |
| 5. #349×C179 | C2 | semidirect |
| 14. #19153053 | C22 | semidirect |
| 18. M32×C179 | C22 | semidirect |
| 93. D179 | #349 | direct (N × H) |
| 94. C179 | C2×#349 | semidirect |
| 100. #349 | D179 | direct (N × H) |
| 112. M32 | C2×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D179 | 2 |
| M32×D179 | 2 |
| #26038221 | 2 |
| #26038220 | 2 |
| #349×C179 | 2 |
| C2×#349 | 179 |