Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C4⋊#13089685 | C2 | semidirect |
| 4. #26042145 | C2 | semidirect |
| 61. C2×C4×C181 | M16 | semidirect |
| 84. C181 | #1851 | semidirect |
| 143. C2×C4 | #15668459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668459 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×#19153873 | 2 |
| #26042145 | 2 |
| #26041126 | 2 |
| #1851 | 181 |