Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C71 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ #117×C71 ◁ #405×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C71×#3176 | C2 | semidirect |
| 2. C71×#2228 | C2 | semidirect |
| 3. C71×#2218 | C2 | semidirect |
| 4. C71×#2215 | C2 | semidirect |
| 5. C71×#2206 | C2 | semidirect |
| 6. C71×#2151 | C2 | semidirect |
| 99. #33825 | C71 | direct (N × H) |
| 104. #3176 | C2×C71 | semidirect |
| 105. #2228 | C2×C71 | semidirect |
| 106. #2218 | C2×C71 | semidirect |
| 107. #2215 | C2×C71 | semidirect |
| 108. #2206 | C2×C71 | semidirect |
| 109. #2151 | C2×C71 | semidirect |
| 110. C71 | #33825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#3176 | 2 |
| C71×#2228 | 2 |
| C71×#2218 | 2 |
| C71×#2215 | 2 |
| C71×#2206 | 2 |
| C71×#2151 | 2 |
| #33825 | 71 |