Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
350 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 1. #22590567 | C2 | semidirect |
| 2. #22590482 | C2 | semidirect |
| 4. #22586389 | C2 | semidirect |
| 5. #22586304 | C2 | semidirect |
| 74. Q16×C71 | SD16 | semidirect |
| 142. C71 | #12370 | semidirect |
| 203. Q16 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590567 | 2 |
| #22590482 | 2 |
| #22587729 | 2 |
| #22586389 | 2 |
| #22586304 | 2 |
| D4⋊(C71⋊C16) | 2 |
| D4×Q16×C71 | 2 |
| #12370 | 71 |