Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3694 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 3694 conjugacy classes of subgroups — too many to draw. Only its 827 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D71 |
| commutator, socle, cosocle | C23×C71 | C25 |
| Frattini | C23 | C24×D71 |
| Fitting | C2×#376×C71 | C2 |
| hypercenter | C2×#376 | D71 |
| hypocenter | C71 | #34641 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17986549 | C2 | semidirect |
| 2. #22594450 | C2 | semidirect |
| 3. #22594446 | C2 | semidirect |
| 4. #22594442 | C2 | semidirect |
| 5. #22591621 | C2 | semidirect |
| 6. C2×#376×C71 | C2 | semidirect |
| 35. C2×C42×C71 | D4 | semidirect |
| 96. C2×#376 | D71 | semidirect |
| 97. C71 | #34641 | semidirect |
| 126. C2×C42 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986549 | 2 |
| #22594450 | 2 |
| #22594446 | 2 |
| #22594442 | 2 |
| #22591621 | 2 |
| C2×#376×C71 | 2 |
| #34641 | 71 |