Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
474 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#15668436 | C2 | semidirect |
| 3. C2×#19153736 | C2 | semidirect |
| 4. #26041034 | C2 | semidirect |
| 5. #391×C181 | C2 | semidirect |
| 31. C2×#13089678 | D4 | semidirect |
| 35. C2×Q8×C181 | D4 | semidirect |
| 63. C2×C4×C181 | SD16 | semidirect |
| 89. C181 | #2014 | semidirect |
| 94. #391 | D181 | semidirect |
| 112. C2×Q8 | D724 | semidirect |
| 152. C2×C4 | #15668436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668436 | 2 |
| C2×#19153813 | 2 |
| C2×#19153736 | 2 |
| #26041034 | 2 |
| #391×C181 | 2 |
| #2014 | 181 |