Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22587226 | C2 | semidirect |
| 3. #22586413 | C2 | semidirect |
| 4. #22586301 | C2 | semidirect |
| 5. #22586300 | C2 | semidirect |
| 6. #22586258 | C2 | semidirect |
| 7. C8×D8×C71 | C2 | semidirect |
| 58. D8×C71 | M16 | semidirect |
| 114. C8×D8 | D71 | semidirect |
| 119. C71 | #12073 | semidirect |
| 163. D8 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556069 | 2 |
| #22587226 | 2 |
| #22586413 | 2 |
| #22586301 | 2 |
| #22586300 | 2 |
| #22586258 | 2 |
| C8×D8×C71 | 2 |
| #12073 | 71 |