Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 3. #26038266 | C2 | semidirect |
| 4. #26038244 | C2 | semidirect |
| 5. #26038242 | C2 | semidirect |
| 7. #367×C179 | C2 | semidirect |
| 66. C179 | #2235 | semidirect |
| 71. #367 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038681 | 2 |
| #107×D179 | 2 |
| #26038266 | 2 |
| #26038244 | 2 |
| #26038242 | 2 |
| (C2×D179)⋊C16 | 2 |
| #367×C179 | 2 |
| #2235 | 179 |