Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
608 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22601313 | C2 | semidirect |
| 2. #22590588 | C2 | semidirect |
| 3. #22590373 | C2 | semidirect |
| 4. #22590372 | C2 | semidirect |
| 5. C16×Dic142 | C2 | semidirect |
| 6. C4×D1136 | C2 | semidirect |
| 7. D16×Dic71 | C2 | semidirect |
| 8. C71×#2246 | C2 | semidirect |
| 82. C16×C71 | #41 | semidirect |
| 101. Dic142 | D16 | semidirect |
| 128. #2246 | D71 | semidirect |
| 134. C71 | #33958 | semidirect |
| 208. C16 | #11765864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601313 | 2 |
| #22590588 | 2 |
| #22590373 | 2 |
| #22590372 | 2 |
| C16×Dic142 | 2 |
| C4×D1136 | 2 |
| D16×Dic71 | 2 |
| C71×#2246 | 2 |
| #33958 | 71 |