Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
118 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C71 | #102 |
| commutator | C8 | C2×C16×C71 |
| Frattini, cosocle | C4×C16 | C22×C71 |
| socle | C2×C71 | D4⋊C16 |
| prime radical | #135×C71 | C8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C71 ◁ C2×C16×C71 ◁ C4×C16×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C71×#1422 | C2 | semidirect |
| 3. C71×#1397 | C2 | semidirect |
| 54. #7382 | C71 | direct (N × H) |
| 59. #1422 | C2×C71 | semidirect |
| 60. #1397 | C2×C71 | semidirect |
| 61. C71 | #7382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2170 | 2 |
| C71×#1422 | 2 |
| C71×#1397 | 2 |
| #7382 | 71 |