Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#19153846 | C2 | semidirect |
| 3. C2×#19153804 | C2 | semidirect |
| 4. #26041289 | C2 | semidirect |
| 5. C2×#19153732 | C2 | semidirect |
| 6. #26041039 | C2 | semidirect |
| 7. C2×#104×C181 | C2 | semidirect |
| 35. C2×Dic362 | D4 | semidirect |
| 47. #15668433 | D4 | semidirect |
| 68. C42×C181 | D4 | semidirect |
| 131. C181 | #2004 | semidirect |
| 136. C2×#104 | D181 | semidirect |
| 200. C42 | C22⋊D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153846 | 2 |
| #26041843 | 2 |
| C2×#19153804 | 2 |
| #26041289 | 2 |
| C2×#19153732 | 2 |
| #26041039 | 2 |
| C2×#104×C181 | 2 |
| #2004 | 181 |