Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
732 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 3. #22588895 | C2 | semidirect |
| 4. #22588211 | C2 | semidirect |
| 6. C42×C71⋊C8 | C2 | semidirect |
| 7. C71×#1839 | C2 | semidirect |
| 76. C42×C71 | M16 | semidirect |
| 101. C71⋊C8 | #126 | semidirect |
| 123. #1839 | D71 | semidirect |
| 127. C71 | #21666 | semidirect |
| 196. C42 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556122 | 2 |
| #22588944 | 2 |
| #22588895 | 2 |
| #22588211 | 2 |
| #22588120 | 2 |
| C42×C71⋊C8 | 2 |
| C71×#1839 | 2 |
| #21666 | 71 |