Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
908 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C71 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| socle | C2×C71 | #2397 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C22×C8×C71 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C71×#2955 | C2 | semidirect |
| 2. C71×#2930 | C2 | semidirect |
| 3. C71×#2098 | C2 | semidirect |
| 4. C71×#2091 | C2 | semidirect |
| 5. C71×#2017 | C2 | semidirect |
| 6. C71×#2010 | C2 | semidirect |
| 7. C71×#1747 | C2 | semidirect |
| 50. #97×C71 | D4 | semidirect |
| 51. C4×C8×C71 | D4 | semidirect |
| 119. #23795 | C71 | direct (N × H) |
| 124. #2955 | C2×C71 | semidirect |
| 125. #2930 | C2×C71 | semidirect |
| 126. #2098 | C2×C71 | semidirect |
| 127. #2091 | C2×C71 | semidirect |
| 128. #2017 | C2×C71 | semidirect |
| 129. #2010 | C2×C71 | semidirect |
| 130. #1747 | C2×C71 | semidirect |
| 131. C71 | #23795 | direct (N × H) |
| 174. #97 | D4×C71 | semidirect |
| 175. C4×C8 | D4×C71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C71×#2955 | 2 |
| C71×#2930 | 2 |
| C71×#2098 | 2 |
| C71×#2091 | 2 |
| C71×#2017 | 2 |
| C71×#2010 | 2 |
| C71×#1747 | 2 |
| #23795 | 71 |