Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
602 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22598920 | C2 | semidirect |
| 2. #22590590 | C2 | semidirect |
| 3. #22590565 | C2 | semidirect |
| 4. #22590427 | C2 | semidirect |
| 5. #22590186 | C2 | semidirect |
| 6. C4×C16×D71 | C2 | semidirect |
| 7. C71×#2252 | C2 | semidirect |
| 76. C16×C71 | #41 | semidirect |
| 96. C4×D71 | D16 | semidirect |
| 123. #2252 | D71 | semidirect |
| 129. C71 | #33733 | semidirect |
| 198. C16 | #11765866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598920 | 2 |
| #22590590 | 2 |
| #22590565 | 2 |
| #22590427 | 2 |
| #22590186 | 2 |
| C4×C16×D71 | 2 |
| C71×#2252 | 2 |
| #33733 | 71 |