Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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⋊C4×D181 | C2 | semidirect |
| 3. C2×#19153738 | C2 | semidirect |
| 4. C2×#19153736 | C2 | semidirect |
| 5. C2×#19153728 | C2 | semidirect |
| 6. #26041041 | C2 | semidirect |
| 7. #340×C181 | C2 | semidirect |
| 14. #19153791 | C4 | semidirect |
| 36. C2×D724 | C2×C4 | semidirect |
| 52. C4⋊Dic181 | D4 | semidirect |
| 63. C4⋊C4×C181 | C2×C4 | semidirect |
| 64. C4⋊C4×C181 | D4 | semidirect |
| 130. C2×D181 | #102 | semidirect |
| 148. C181 | #1874 | semidirect |
| 156. #340 | D181 | semidirect |
| 211. C4⋊C4 | C4×D181 | semidirect |
| 212. C4⋊C4 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153791 | 2 |
| C2×C4⋊C4×D181 | 2 |
| C2×#19153738 | 2 |
| C2×#19153736 | 2 |
| C2×#19153728 | 2 |
| #26041041 | 2 |
| #340×C181 | 2 |
| #1874 | 181 |