Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
552 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22601346 | C2 | semidirect |
| 3. #22590596 | C2 | semidirect |
| 4. #22590386 | C2 | semidirect |
| 5. #22590381 | C2 | semidirect |
| 6. C4×#14556073 | C2 | semidirect |
| 7. Q8×C16×C71 | C2 | semidirect |
| 72. C16×C71 | #41 | semidirect |
| 74. Q8×C71 | SD32 | semidirect |
| 112. Q8×C16 | D71 | semidirect |
| 114. C71 | #33959 | semidirect |
| 179. C16 | #11765866 | semidirect |
| 183. Q8 | #14556073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601346 | 2 |
| #22601315 | 2 |
| #22590596 | 2 |
| #22590386 | 2 |
| #22590381 | 2 |
| C4×#14556073 | 2 |
| Q8×C16×C71 | 2 |
| #33959 | 71 |