Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
198 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 61 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×#19153761 | C2 | semidirect |
| 2. C2×D2896 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041656 | C2 | semidirect |
| 5. #346×C181 | C2 | semidirect |
| 31. C16×C181 | D4 | semidirect |
| 59. C181 | #2250 | semidirect |
| 65. #346 | D181 | semidirect |
| 91. C16 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153761 | 2 |
| C2×D2896 | 2 |
| #26041663 | 2 |
| #26041656 | 2 |
| #346×C181 | 2 |
| #2250 | 181 |