Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 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 |
|---|---|---|
| 1. C2×#17986438 | C2 | semidirect |
| 3. #494×D71 | C2 | semidirect |
| 4. #22590610 | C2 | semidirect |
| 5. #22590595 | C2 | semidirect |
| 6. #22590593 | C2 | semidirect |
| 7. #22590592 | C2 | semidirect |
| 8. C4×#14556067 | C2 | semidirect |
| 9. C71×#2248 | C2 | semidirect |
| 64. #14556067 | D4 | semidirect |
| 156. C4×C71 | #510 | semidirect |
| 173. #2248 | D71 | semidirect |
| 177. C71 | #33718 | semidirect |
| 328. C4 | #17986438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986438 | 2 |
| #22598767 | 2 |
| #494×D71 | 2 |
| #22590610 | 2 |
| #22590595 | 2 |
| #22590593 | 2 |
| #22590592 | 2 |
| C4×#14556067 | 2 |
| C71×#2248 | 2 |
| #33718 | 71 |