Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22598892 | C2 | semidirect |
| 3. #22598163 | C2 | semidirect |
| 4. #22594285 | C2 | semidirect |
| 5. #22589551 | C2 | semidirect |
| 6. #22589320 | C2 | semidirect |
| 7. #22588552 | C2 | semidirect |
| 8. #22588153 | C2 | semidirect |
| 9. C71×#1965 | C2 | semidirect |
| 134. M16×C71 | #41 | semidirect |
| 206. #1965 | D71 | semidirect |
| 209. C71 | #25690 | semidirect |
| 314. M16 | #11765864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602214 | 2 |
| #22598892 | 2 |
| #22598163 | 2 |
| #22594285 | 2 |
| #22589551 | 2 |
| #22589320 | 2 |
| #22588552 | 2 |
| #22588153 | 2 |
| C71×#1965 | 2 |
| #25690 | 71 |