Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
196 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C139 | D4 |
| commutator | C4 | C22×C8×C139 |
| Frattini, cosocle | C42 | C23×C139 |
| socle | C22×C139 | C4×D4 |
| prime radical | C2×D8×C139 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C139 ◁ C4×C8×C139 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×D4×C139 | C2 | semidirect |
| 3. #335×C139 | C2 | semidirect |
| 4. D4⋊C8×C139 | C2 | semidirect |
| 5. C82×C139 | C2 | semidirect |
| 18. D8×C139 | C8 | direct (N × H) |
| 31. D4×C139 | C2×C8 | semidirect |
| 42. C8×C139 | C2×C8 | semidirect |
| 43. C8×C139 | D8 | direct (N × H) |
| 58. C139 | C8×D8 | direct (N × H) |
| 59. C8×D8 | C139 | direct (N × H) |
| 61. C8×D4 | C2×C139 | semidirect |
| 62. #335 | C2×C139 | semidirect |
| 63. D4⋊C8 | C2×C139 | semidirect |
| 64. C82 | C2×C139 | semidirect |
| 77. D8 | C8×C139 | direct (N × H) |
| 90. D4 | C2×C8×C139 | semidirect |
| 101. C8 | C2×C8×C139 | semidirect |
| 102. C8 | D8×C139 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×C139 | 2 |
| C8×D4×C139 | 2 |
| #335×C139 | 2 |
| D4⋊C8×C139 | 2 |
| C82×C139 | 2 |
| C8×D8 | 139 |